Passy's World of Mathematics

Free Online Math Worksheets

Posted on July 30, 2011 by Passy

$Pic of homework and a pencil and calculator$
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Need some practice on a Mathematics topic ?

There are plenty of free practice questions on the Internet. Not only are they free, but they have answers available for checking your work.

There are loads of great free worksheet sites for Primary school level mathematics, but the good ones for High School and middle school can sometimes be a bit more challenging to find.

Our review includes some Primary Worksheets, but also focuses on worksheets that are suitable for High School mathematics.

Since these worksheets are either loaded as web pages, or online Adobe PDF documents, they should all work on Apple devices, as well as on PC’s and Laptops.

We found lots of sites on the Internet for Math Worksheets, and this review features what we consider to be ten of the best worksheet sites on the web.

If you know any other great worksheet sites not listed here, then please contact us via our email address on the side bar.

Kuta Software

This is a great website with worksheets for all of the common mathematics topics from Primary through to Middle School.

We love this website, it is well laid out with all of the sheets as PDFs with answers supplied. Well worth a visit.

http://www.kutasoftware.com/freemain.html

Online Math Learning

This site has lots of worksheets that we fill in on the screen and then click a button at the bottom of the sheet to check the answers.

As a result the worksheets are not really printable.

We really like this site because it covers all of the topics required from Primary through to Middle School mathematics.

http://www.onlinemathlearning.com/math-worksheets.html

TeAchnology

This site has lots of printable worksheets covering grades 1 to 8, all with answers.

Topics covered include basic numeracy, Measurement, Geometry, Statistics, Equations, and many others.

Some worksheets are in the main area, and others are in the grade specific links on the page.

http://www.teach-nology.com/worksheets/math/

Math Worksheets Go

This site covers Algebra, Geometry, and Trigonometry for High School students, and does not cover other topics.

To get to worksheets, we have to click on a download button to get to the web oage that has the worksheet.

Each worksheet has a lesson, that usually includes a Video, and then the worksheet practice questions, followed by an answer sheet.

http://www.mathworksheetsgo.com/

Math Worksheets for Kids

This site has lots of printable web page worksheets covering Grades 1 to 8, all with answers.

Topics covered include basic numeracy, Measurement, Geometry, Statistics, Equations, and many others.

There are also separate difficulty level worksheets on topics like “Median” and others, that range from simple to hard.

http://www.mathworksheets4kids.com/

Free Math Worksheets

This is a great site for High School Mathematics PDF worksheets. Each worksheet loads up as a PDF in Adobe Acrobat and has answers.

It does not cover all maths topics but has plenty of worksheets for Algebra and Graphs up to middle school level.

http://www.math-worksheet.org/

Fun Maths

This website has free High School level worksheets for Geometry, Algebra, Trigonometry, Statistics, Measurement, and Number.

However, some topics are not comprehensive. For example, Statistics only covers Probability, and not Mean, Median, Mode.

Most of the worksheets we looked at do not have answers, and so teachers would have to workout solutions.

http://www.funmaths.com/worksheets/index.htm

EZ School

We really like this site, because it has worked solutions for most of the worksheets. The sheets are on web pages but can be printed out.

Level covered is basic numeracy, through to lower middle school. (Although the site says they cover Grades 6 to 12, we could not find anything past Grade 8 level when we looked on the site.

Topics include Mean Median Mode, Equations, and Exponents.

http://www.ezschool.com/EZSheets/

Math Drills

“Math Drills” is believed to have over 10,000 free math worksheets with answer keys.

The worksheets are PDF documents which usually have one page of questions, immediately followed by a page with the answers.

The range of worksheets currently appears to cover basic numeracy through to lower middle school level, including Algebra, Geometry, Measurement, and others.

http://www.math-drills.com/

Free Math Worksheets

This site covers basic numeracy, with the occasional advanced topics like Quadratic Equations.

There is a generator page that needs to be filled in with information, and then the worksheet is generated.

The worksheets are printable web pages which usually have one page of questions, immediately followed by a page with the answers.

http://www.freemathworksheets.net/

Home School Math

This site covers basic numeracy, and is mainly primary school level through to the beginning of High School.

The worksheets are printable web pages which usually have one page of questions,and then we can click at the bottom of this page to open up the answers page in a new window on our web browser.

http://www.homeschoolmath.net/worksheets/

Math Worksheets Land

Math Worksheets Land is a free worksheets site ran by a retired middle school teacher in the USA with over 30 years teaching experience.

She is very passionate about her work, and is continually adding new material to the site.

Notes, Lessons, and Worksheets with Answers in printable PDF form are available for Primary School through to Secondary.

Math Worksheets Land also has a page on Facebook.

This is an excellent site and we recommend that you use the link below to check it out.

http://www.mathworksheetsland.com/

That completes our list of great sites for getting free math worksheets.

Please note that Passy’s World of Mathematics has no financial interest in any of the websites reviewed in this lesson.

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Passy

Fibonacci Sequence in Music

Posted on July 26, 2011 by Passy

Source: http://blog.the-market-toolbox.com

To play music, we use our fingers, and the size of their joints actually forms a mathematical pattern called a “Fibonacci Sequence”.

Leonardo Fibonacci, was born in the 12th century, and studied a sequence of numbers with a special type of rule for determining the next number in the sequence.

He began the sequence with 0,1, … and then calculated each successive number from the sum of the previous two. ( Eg. 0+1=2, 1+2=3, 2+3=5, 3+5=8, etc)

This sequence of numbers is called the Fibonacci Numbers or Fibonacci Sequence.

The Fibonacci numbers are interesting in that they occur throughout both Nature, Art, Engineering, and Music.

Here are the first few numbers of the sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ……

The ratios of these successive numbers leads to interesting spiral patterns that are found in nature:

Image Source: http://ps2pm.files.wordpress.com

Image Source: http://www.onlineinvestingai.com

Image Source: http://www.maths.surrey.ac.uk

Image Source: http://www.creationresearches.com

Source: http://farm1.static.flickr.com

Nature is indeed beautiful, but our main interest here is the maths in music.

The Fibonacci Numbers amazingly form the foundation of music.

The first numbers of the Fibonacci Series (after 0,1) are: 1, 2, 3, 5, 8, 13

There are 13 notes in the span of any note through to its octave.
Eg. For the Octave of C on the piano keyboard shown above, there are
thirteen notes in total : 8 white keys and 5 black keys.

However to play the “scale” of C, we only play the 8 white keys.

A scale is comprised of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords.

We also have harmonising intervals of 3rds and 5ths.

To produce a “third” we play the first note and a note 2 tones higher than this note.

To play an Octave we play the first note, and then a another note 8 tones higher.

Note in all of the above, (which is the basis of music), all of the notes and intervals only use the Fibonacci Numbers 1, 2, 3, 5, 8, and 13.

The series can also be used when composing music to make patterns of notes that are pleasing to the ear. It is claimed that classical composers like Mozart and Bartok used the Fibonacci series in some of their pieces.

For a more in depth look at mathematical symmetries in Music, including use of the Fibonacci Sequence, check out the following excellent webpage from the “Mathematical Institute of the Serbian Academy of Sciences and Arts”.

http://www.mi.sanu.ac.rs/vismath/jadrbookhtml/part42.html

Has the Fibonacci Series ever been used in Rock Music ?

Yes of course it has! Power Chords are actually 5ths intervals, Triad chords use 1,3,and 5, Octaves use 8ths: these are all Fibonacci numbers !

Slideshare Presentation About Music Math

The following Slideshare presentation is all about the Fibonacci Sequence, including the Golden Ratio, in nature as well as music.

[slideshare id=1798646&doc=goldenmusic3-090801102457-phpapp01]

If you have an Apple device which is not displaying this slideshow properly, then click the following link:

http://www.slideshare.net/rubiz/golden-music

Music Math Videos

Here is a fun outdoor piano that was built in Sweden. People were able to do their own experiments with different sequences of the Fibonacci based notes. The results were very entertaining.

[youtube=http://www.youtube.com/watch?v=2lXh2n0aPyw&w=500&h=304]

Here is some music and images, that are not Fibonacci Sequences, but instead involve “Fractals”, which are another type of really interesting mathematical pattern. The following chillout video is a Montage of “Mandelbrot” and “Julia” Sets.

[youtube=http://www.youtube.com/watch?v=LPW1xgPrdyA&w=500&h=405]

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Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.

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Enjoy,
Passy

Posted in Fibonacci Sequence in Music, Math Applications, Math in Music, Math in the Real World | Tagged Fibonacci, Fibonacci Sequence, Fibonacci Sequence Applications, Fibonacci Sequence in Music, golden ratio, golden ratio in music, Math in Music, ratio | 11 Comments

Weight Training Mathematics

Posted on July 24, 2011 by Passy

Image Source: http://sp.life123.com

Suppose we want to do some weight training in the gym to help us with sport and be healthy. We might need to get a few things worked out first.

How do we know how much weight to lift for a given exercise?
How do we know how many times (“repetitions”) we should do?
How do we know how many sets of exercises to do ?
How do we know how long to rest in between sets ?
How many times should we go to the gym a week ?
How long should we rest between trips to the gym ?

There is no ready made mathematical answer to all of these questions.

We need to hire a professional trainer to work out a starting point for us, and that will be money well spent.

However we can also do some internet research and a bit of mathematics, to find out some relevant information ourselves.

While it is good to do some math to determine the training weights that you can use, you should always check with a personal trainer or gym staff, before commencing your program.

The contents of this post are a mathematical review of some websites for weight training, and are definitely not weight training advice for someone to set up their own training program.

Here at Passy World we do regular weights training, but we had our program set up by professional staff at a gym. We recommend that you always do the same.

Let’s look at some of the mathematics of weight training.

Here is a short YouTube video which mentions some of the mathematics involved with weight training.

[youtube http://www.youtube.com/watch?v=Kv-euC8Qmjs]

As demonstrated in the video, the key to each exercise is the “repetition” which is the full motion we do to complete the exercise once.

“Brian Mac – Sports Coach” is a brilliant website about weight training, and the source of most of the material which follows in this post.

http://www.brianmac.co.uk/weight.htm

We highly recommend visiting the above link for a great overview of muscle strength development and sports training.

On the “Brian Mac” site, ranges of values for recommended repetitions are given, depending on the type of training that the person needs to do.

This is summarized in the following table.

The types of training indicated in the above table, as per the “Brian Mac” site are as follows:

Strength Endurance

The aim is to develop muscles that are able to to produce repeated contractions under conditions of fatigue. This requires high repetitions (15+) with light loading (30-50% of 1RM). Appropriate for field sports, rowing and martial arts.

Power

The aim is to develop fast powerful movements. This requires medium number of repetitions (6-10) with medium to heavy loading (70-80% of 1RM). Appropriate for power based events e.g. sprinting, jumping (long jump), throwing (Javelin).

Maximum Strength

The aim is to enable maximum loads to be lifted. This requires low number of repetitions (1-5) with heavy loads (80-100% of 1RM). Appropriate for Power Lifting, Olympic Lifting, Shot Putt.

In the table shown previously, all weight to be lifted is expressed as a percentage of the “1RM” weight value which is set at 100%.

The 1RM weight is the maximum weight we can lift for a specific exercise, where the weight is so heavy that we are only able to do one repetition of that weight. We are not strong enough to do a second lift of that weight.

As we train and get stronger, this 1RM value may become larger, and so it needs to be recalculated from time to time.

But how do we determine the 1RM weight for a particular exercise?

The “Brian Mac” site has a very nice online calculator that looks like this:

Three estimates are provided by this calculator:

Novice – an adult with less than 1 year of regular weight training
Experienced – an adult with 1 to 2 years of regular weight training
Advanced – an adult with more than 2 years of regular weight training

Once we have determined the weight we should lift for 1RM (One Repetitition Maximum) at 100% training weight from the calculator, we can then work out what weight we would need to do for different amounts of repititions, according to the training program we are following: Strength, Power, or Endurance.

For example, Let’s say we obtained 120kg for Military Bench Press as our 1RM from the calculator. If we want to do Endurance Training, then we need to consult our training table.

The table shows that if we want to do 14 reps per exercise for Endurance, then we need to have our barbell weight set at 65% of 1RM.

So our required weight is calculated as 65% of 120kg = 0.65 x 120 = 78kg.

For Endurance training we need to Military Bench Press 78kg of weight.

But what if we want to determine the 1RM for an exercise that is not in the Brian Mac calculator, such as Bicep Curls.

Image Source: http://munfitnessblog.com

What we need to do is work out the maximum weight we could manage for several reps, until such point as our muscles are fatigued, and we cannot lift the weight any more.

For example, to do a 1 rep max test for the bicep curls, we might lift a 40kg barbell and discover that we can only lift the weight 6 times until our muscles are completely fatigued.

From our previous table we know that 6 repetitions represents 85% of the 1RM weight value.

85% of 1RM is 40kg (Divide both sides by 85)
1% = 40 divided by 85
1% = 0.470588 (Now Multiply both sides by 100)
100% = 47 kg

So our calculated 1RM value for us doing 1 rep of bicep curls is 47kg.

To check the mathematics we have done, we can use an Online 1RM Calculator.

There is a very good calculator for determining the 1RM value, (as well as the training percents), at the following link:

http://www.exrx.net/Calculators/OneRepMax.html

Interestingly, when we use this calculator for our 6 reps of 40kg Bicep Curls, the answer given is 46kg and not 47kg.

There are several slightly different 1RM math formulas, made by different researchers. This is discussed on Wikipedia, and the common formulas are by Brzycki, Beachle, Epley, Lander, Lombardi, and others.

The Online Calculator appears to be using the Brzycki formula:

1RM = Weight / (1.0278 – (0.0278 x Reps))

which is the most commonly used formula by most Sports Scientists and Personal Trainers.

The % Table we have been using in this blog is only an approximation, with rounded off percents. It is therefore not suitable for calculating accurate 1RPM values.

We need to use the Brzycki formula to work out our 1RM correctly. This is simple to do, and involves some basic Algebra substitution.

For our Bicep Curls we have:
Weight = 40
Reps = 6

1RM = Weight / (1.0278 – (0.0278 x Reps))
= 40 / (1.0278 – (0.0278 x 6))
= 40 / 0.861
= 46.46
= 46kg.

Now that we know the 1RM for our Bicep Curls is 46kg:

If we want to do “Power Training” then we could work at
12 reps using 70% of 46 = 12 reps using a 32kg weight.

And if we wanted to do “Endurance Training” for our bicep curls, we could work a set of 14 reps using 65% of 46 = 14 reps using a 30kg weight.

You may be wondering what exactly are bicep curls exercises ?

“Expert Village” on YouTube have some really good YouTube videos on how to do different weight training exercises.

So if you forgot some of the things your personal trainer showed you at the Gym, then find a video on YouTube to watch.

Here is a great example video by Expert Village on bicep curls.

[youtube http://www.youtube.com/watch?v=o2oCT5tZMA4]

Finally, let’s take a look at some of the Mathematics involved in Olympic Weight Lifting.

Competition Weight Lifting is all about overcoming the force of gravity in the most efficient way possible. This involves applying some specific mathematical geometry and alignment between the weight being lifted and the the person lifting the weight.

Here is an excellent science documentary video, which explains the mathematics and geometry very clearly.

Image Source: http://ph.cdn.photos.upi.com

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Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.

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Enjoy,
Passy

Posted in Math Applications, Math in the Real World, Online Calculators, Weight Training Math | Tagged mathematics of weight lifting, mathematics of weight training, weight lifting math, weight lifting maths, weight training math | 15 Comments

Free Online Math Tests Review

Posted on July 23, 2011 by Passy

Kids on OLPC laptops Image Source: http://www.monitoringsoftwareblog.com The Internet is an incredible resource for mathematics learning tools. And after we have done some learning, we need to test how much has been retained and properly understood. What better way to do this than to take a quick online test and get immediate feedback. “Online Tests” are onscreen interactive tests, where we can type an answer into the computer. The computer then immediately corrects all of our questions and gives us our score. There are many websites that have free PDF Practice Tests for National testing in the UK and USA, but these are not corrected by the computer online, and so we consider these to be worksheet type resources rather than online tests. In this post we look at ten great websites that have free online tests for Mathematics. We have used these online tests on an Apple iPad device, and most of them work. The only ones which do not seem to work at all on iPad (as of 25/7/11) are the “That Quiz” and “Math Tests” sites. The probable reason being that Apple devices do not support Flash or Java. To get to each site, use the text link supplied at the end of each mini review. Click this text link to go to the site – do not click the banner image. Free Math Test This site is really good and simple to use. It covers basic mathematics up to Averages and Integers, Substitution, Order of Operations. There do not seem to be any Fractions, Decimals, Percentages, Ratios, or Solving Equations questions. This site allows a person to choose the level of difficulty, and the number of questions they want to do. http://www.freemathtest.com/ That Quiz This covers a lot of mathematics right up to Trigonometry and Calculus. This site also allows a person to choose the level of difficulty, and the number of questions they want to do. It is a great site and worth using. http://www.thatquiz.org/ See our full review of “That Quiz” on a separate post at the following link. http://passyworldofmathematics.com/online-testing-with-that-quiz/ Math Tests This site has a great range of online tests, but a selected test can take a minute or two to load in, so be patient. It also does not appear to allow selection of the number of questions or their difficulty, and seems to default to 10 questions for each test with a 30 minute time limit that is enforced by an onscreen timer. http://www.math-tests.com Soft Schools This site has plenty of basic math tests. However it does also have some good middle school tests for Algebra such as solving one variable equations. It does not appear to allow selection of the number of questions or their difficulty, and seems to default to 10 questions Other things of interest on this site are as follows. A nice Quadratic grapher with value sliders at: http://www.softschools.com/math/algebra_1/quadratic_equation_graph/ and a similar straight line graph simulator at: http://www.softschools.com/math/algebra_1/straight_line_graph/ A set of calculators at: http://www.softschools.com/math/online_calculators/ The site also has Worksheets, but for some of them you need to be a registered user. (Registration appears to be free). The homepage for Soft Schools is as follows: http://www.softschools.com/ Amby Math Tests This site has a number of basic skills math tests that can be done online. A mini lesson is given at the start of each test. It does not appear to allow selection of the number of questions or their difficulty, and the number of questions between different tests varies. http://amby.com/tests/math/ Math Goodies This site does not have quizes that you can directly go to, but has lessons on topics, that most times have a short online quiz at the end of them. The topics are on basic math, and do not include middle school topics like Trigonometry, Equations, and Algebra. This site does not allow selection of the number of questions or their difficulty, and the number of questions in an end of lesson quiz varies. As well as lessons with Quizes at the end of them, the site also has plenty of worksheets. It is an excellent site, and one of our favorites. Check out all of the lessons at the link below. http://www.mathgoodies.com/lessons/ BBC Maths This site is like Maths Goodies, and has lesson lists and the lessons contain online tests. It does not allow selection of the number of questions or their difficulty, and the number of questions at the end of a lesson always appears to be 10. This is a great site and one of our favorites. Check out the comprehensive list of lessons covering basic number through to Trigonometry, Algebra, and Equations. So the BBC cover primary through to middle school for free online resources, and do it as good as any site we have seen. http://www.bbc.co.uk/schools/websites/11_16/site/maths.shtml Khan Academy Saving one of the best for last, the Kahn Academy is an awesome website of free online Math Learning resources. There are lots of videos, but to do online practice tests, we need to click on the “Practice with an Exercise” button, and then navigate down the left had side of the page to the topic we want to practice. The practice sessions have scoring, and you can ask for hints, or watch a video if you are struggling with the test. This site does not appear to allow selection of the number of questions or their difficulty http://www.khanacademy.org/ Cool Math This is a great site that has lessons, games and quizes for math from Primary through to the end of middle school. We have found that students really like this site for the math games and activities it has. The online testing can be found under the “Practice Problems” link. Here we usually get problem generators, so we can do as many questions as we like, on a very specific part of math, and get an answer when we need it. For example check out this typical one at a time question generator. http://www.coolmath.com/crunchers/algebra-problems-solving-equations-1.htm The Cool Math homepage can be found here: http://www.coolmath.com/ My Quizzes CA This site has quizzes that people submit, and so the quality can vary. However there are around 500 online math quizzes on the site. http://www.myquizzes.ca/ So that’s our Top 10 of great Free Math Quiz and Test sites. These are a great way to check up on how your math skills are going, and an excellent tool to use when reviewing for tests. Best of all they are available 24×7, and 100 percent FREE! Please note that Passy’s World of Mathematics has no financial interest in any of the websites reviewed in this lesson. Related Items Free Online Math Videos Free Online Math Worksheets Free Online Graph Makers Free Online Calculators and Converters GeoGebra Online Interactives and Demonstrations Mathwarehouse Interactives Microsoft Mathematics Free App for Windows PC My Virtual Home If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address. Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button. To find out exactly how free subscription works, click the following link: How Free Subscription Works If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page. Enjoy, Passy]]>

Posted in Free Online Math Tests, Online Math Resources, Online Math Tests, Online Math Tools, Online Maths Tests Review, Online Tests and Quizes | Tagged Online Math Tests, Online Math Tests Links, Online Maths Test Links, Online Maths Tests | 8 Comments

Tsunami Mathematics

Posted on July 19, 2011 by Passy

Image Source: http://millicentandcarlafran.files.wordpress.com

In this lesson we look at the Mathematics associated with Tsunami Waves.

During 2011, most of us viewed news reports of powerful and devastating Tsunami waves that were produced by a 9.0 magnitude Earthquake off the shore of Japan.

A Tsunami is actually a series of waves. In the open ocean the waves are not high at all, and can pass under ships with no noticeable effect.

But Tsnamis can travel at the speed of jet aircraft (700 km/hr), and can stretch in length for hundreds of kilometres across the ocean.

As the waves approach land, their energy intensifies, and the height of the wave can increase to as high as 60 meters.

Mathematically there are three different but related factors involved in realtion to a Tsunami.

These are SPEED, HEIGHT, and ENERGY POWER.

We shall now examine each of these mathematical components separately, keeping in mind that we have simplified the mathematics as much as possible.

Detailed mathematical equations of water waves look something like this:

Image Source: http://www.oceanographers.net

These equations require super computers to help work on them.

To see what the full set of real equations look like, as well as a computer model of a Tsunami, check out the following web page:

http://mathworld.wolfram.com/news/2005-01-14/tsunamis/

We have simplified the mathematics greatly in the material which follows.

Let’s start with Tsunami speed.

Mathematical Speed of a Tsunami

In the open Ocean the speed of a Tsunami is approximately:

Speed = The Square root of (9.8 x Water Depth)

The 9.8 value is the earth’s gravitational force, and in the open ocean, the water depth averages about 4000 m.

Image Source: http://2.bp.blogspot.com

Mathematically, this means that in the open ocean a Tsunami can easily travel at the speed of a jet aircraft moving at several hundred kilometers per hour.

(Source: http://terrytao.wordpress.com/2011/03/13/the-shallow-water-wave-equation-and-tsunami-propagation/)

However, when the Tsunami approaches close to a shoreline, and the depth decreases to a few hundred meters, the speed slows down, (as per the above maths equation), to a few hundred km / hr.

As the Tsunami waves slow down, they move closer together and rise in height. They can reach heights up to 60 metres when they arrive on shore, with speeds of 250 km/hr, producing a huge destructive force.

Mathematical Height of Tsunami Waves

As the Tsunami approaches shore, the water depth decreases, causing the Tsunami to slow down, at a rate proportional to the square root of the depth.

Unfortunately, “wave shoaling” then forces the Amplitude (Height) to increase at the opposite rate of:

Height is proportional to 1 divided by square root of water depth.

Eg. If the water depth is 400m and then decreases to 4m, then we have a 1/20 Amplitude rising to a 1/2 Amplitude, which means the wave will suddenly become 10 times higher. So a 1m high wave one km from the shoreline, suddenly becomes 10 metres high as it gets to the shoreline.

The following diagram shows this Mathematics of the Tsunami height increasing:

Image Source: http://www.waikatoregion.govt.nz

The following picture shows a 10 meter high Tsunami hitting the coast of Japan.

Image Source: http://www2.registerguard.com

Mathematical Power of Tsunamis

The POWER of any wave is mathematically related to the square root of how LONG the wave is.

Energy Power is proportional to the square root of wave Length.

(Source: http://plus.maths.org/content/os/issue34/features/tsunami/index)

Normal waves at a beach on a rough day might look something like this:

Image Source: http://cdnimages.magicseaweed.com

Long Waves at an Ocean beach produce much more powerful “surf” waves, because they have much more side to side length; and “wavelength” distance between successive waves.

Image Source: http://cdnimages.magicseaweed.com

In Victoria Australia, beaches with Long waves that are very powerful include: Kilcunda, Woolamai, Venus Bay, and to a much lesser extent Inverloch.

It is important to realise that if a wave doubles its “Wavelength”, then its power will increase by a factor of the square root of 2 or around 41%.

So the increase in Power is not double when we double the length, but is around 1 and a half times more powerful.

Tsuanamis are waves that are hundreds of kilometers long, (and can have a “wavelength” between crests of 200km), and so the energy power they unleash is tens of thousands of times greater than that of even the biggest crushing surf or storm waves.

And how did these Tsunami waves become so long?

Well we need to remember that the earthquake that produced them unleashed a mammoth amount of energy into the ocean. And this energy produces waves which are hundreds of kilometres long. Waves that are much longer than the winds from any big storm could ever produce.

Image Source: http://www.washingtonpost.com

The following video shows the long Tsumani waves hitting Japan in March 2011.

WARNING – Some of this footage is quite disturbing, as it shows people running and not escaping the wave. Proceed with caution if showing these Tsunami videos to middle school students.

[youtube=http://www.youtube.com/watch?v=w3AdFjklR50&w=540&h=435]

This next video that shows the power of these huge Tsunami waves as they hit the shore of Japan in 2011.

[youtube=http://www.youtube.com/watch?v=TRDpTEjumdo&w=540&h=435]

As can be seen, the Tsunami is more like a huge surge of water, rather than one big crashing wave. Also evident in these videos is that there are several Tsunami waves coming one after each other. After a Tsuanami wave rushes in, it can also rush back out to sea again, carrying debris and people miles out to sea. In addition, it is quite possible for more giant waves to keep arriving, even an hour after the first one has hit.

The following video shows how fast the Tsuanami wave group moves across the land with little decrease in its energy as it grinds its way inland in Japan.

[youtube=http://www.youtube.com/watch?v=OJoyXzQXXjs&w=540&h=334]

In this next video the Tsunami overcomes the protective sea wall that had been built around a Japanese town:

[youtube=http://www.youtube.com/watch?v=CFvy2Lb_wEw&w=540&h=334]

So that’s a bit of simplified Mathematics about the massively damaging power of Tsunamis. Hopefully it adds to our understanding of the world around us, even if it is only useful the next time we happen to visit a surf beach. Let’s hope none of us ever do any first hand investigation of the mathematics of a Tsunami wave.

MAV Conference PowerPoint

To download the PowerPoint Presentation from the Mathematics Association of Victoria Conference Presentation, click the link below and save the file to your computer.

Mathematics of Tsunamis

Click the link below to download this 2MB PPT File:

http://passyworldofmathematics.com/MAVconfPPTs/TsunamiMathPPTv1.pptx

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Posted in Math in the Real World, Ocean Mathematics, Tsunami Mathematics | Tagged can you surf a tidal wave, can you surf a tsunami, energy of tsumami wave, equations for tsumami, how tsumamis work, mathematics of tidal waves, mathematics of tsumami, mav conference ocean mathematics, ocean mathematics, ocean wave mathematics, passy world ocean mathematics, tidal wave disaster, tidal wave equations, tidal wave math, tidal wave science, tsumami disaster, tsumami energy equation, tsumami equations, tsumami math, tsumami math equations, tsumami mathematics, tsumami maths, tsumami maths equations, tsumami science, tsumami wave model, tsunami height equation, what makes tidal waves powerful | 11 Comments

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