Maths arts

Science, Maths & Technology

What is sound?

Updated Friday 24th February 2017

We hear it all the time - but what is sound?

Unlike our eyes, we cannot close our ears, so it can be argued that hearing is one of our most important senses. We are continually subjected to a huge number of different types of sound.

Some are pleasant and desirable, such as speech and music, while others are unwanted and annoying, such as machinery and road noise.

But just what is sound? How is it produced and how does it travel? And, indeed, how is sound heard?

Any sound, whatever it may be, is caused by something vibrating. In other words, by something which is moving back and forth, either in a regular manner or in a random manner, about the position it occupies when at rest. The source of the sound may be a car engine, a burglar alarm or a bird singing. Whatever it is, some part of it must be vibrating for it to produce sound.

In fact, it is easy to detect the vibrations of many sources of sound. If you touch your throat while singing or speaking, you can feel the vibrations of your vocal cords. Similarly, a hi-fi loudspeaker vibrates strongly especially when the volume is turned up. By lightly touching the speaker cone, you can feel its vibrations as a tingling sensation in your fingertips.

For such vibrations to be heard as sound, there must be a medium through which they can travel from the vibrating source to the ear. For example, sound travels clearly through water, as any swimmer can testify, and it also travels exceptionally well through metal. Most of the sounds we hear, however, are transmitted through air.

The vibrations of a sound source cause the neighbouring air molecules to be alternately squeezed together and pulled apart. These air molecules then push and pull against their neighbours which, in turn, push and pull against their neighbours.

In this way, a series of compressions (regions of higher pressure) and rarefactions (regions of lower pressure) is generated which travels away from the vibrating source. This sequence of pressure fluctuations is what we refer to as a sound wave.

When we hear a sound, what our ears are actually doing is converting the rapid fluctuations in air pressure that make up a sound wave into neural impulses. The human ear comprises three fairly distinct sections; the outer ear, the middle ear and the inner ear.

The outer ear funnels sound waves through the ear canal to the middle ear. In the middle ear, the sound waves meet the tympanic membrane (eardrum) causing it to vibrate.

Three bones in the middle ear - the malleus, the incus and the stapes - transmit vibrations from the eardrum to the inner ear. In the inner ear, the cochlea converts the vibrations to nerve impulses.

Finally, the auditory nerve receives the messages which have been translated into nerve impulses by the ear and carries them to the brain where they are interpreted as sound.

Maths and music

How is an instrument tuned?

To tune any two instruments, the sound waves from both of them must be at the same frequency. If the frequencies differ very slightly, the two sound waves interfere, making another sound wave that undulates in volume or 'beats'.

The beat frequency is the number of volume undulations heard per second. It is found by subtracting the lower frequency from the higher one. When two instruments are in tune, the beat frequency should be zero. This is an extremely useful tool for tuning instruments accurately by ear.

Most people can usually tell whether an instrument is in tune or not without knowing the underlying science.

Three types of instrument

Stringed instruments 
The pitch of a stringed instrument depends on the tension and the length of the string. In most stringed instruments the pitch gets higher when the player moves their hand closer to the bottom of the string making the vibrating area shorter. However, Mike's double bass depended on changing the tension of the string to obtain each note.

In many stringed instruments, the strings themselves only produce a small fraction of the sound that is heard. The rest is due to resonance from the body of the instrument vibrating in sympathy with the strings. Mike's double base had a huge box and a long string which gave it a very low pitch.

MATHS IN DAILY LIFE

1.Math comes in handy when travelling and shows up in various ways from estimating the amount of fuel you’ll need to planning out a trip based on miles per hour and distance traveled. Calculating fuel usage is crucial to long distance travel. Without it, you may find yourself stranded without gas or on the road for much longer than anticipated. You may also use math throughout the trip by paying for tolls, counting exit numbers, checking tire pressure, etc.

Long before GPS and Google Maps, people used atlases, paper road maps, road signs, or asked for directions in order to navigate throughout the country’s highways and byways. Reading a map is almost a lost art, but requires just a little time, orientation, and some basic math fundamentals. Teaching students how to use their math skills to read maps will make them safer travellers and less dependent on technology.

In order to use any map, you must first orient yourself, meaning to find your current position on the map. This will be point A. The simplest way to do this is to locate the town you’re in then the nearby crossroads, intersection or an easily identifiable point such as a bridge, building, or highway entrance. Once you’ve established a starting point, locate where on you want to go (point B). Now you can determine the best route depending on terrain, speed limit, etc.

2.

Daytime Navigation: In the Northern Hemisphere, the sun rises in the east and sets in the west. Depending on the time of day, you can orient yourself based on the sun’s position in the sky. This gets a bit trickier around midday as the sun appears directly overhead at noon. The earth’s rotation around the sun and sun’s position overhead is also the basis for the sundial, Man’s first clock.

Taken from

https://www.thinkthroughmath.com/math-real-life-examples/

MATHS IN DAILY LIFE

When am I ever going to use this?

Variations of this question have echoed through the halls of math classrooms everywhere. Struggling students often become frustrated with complex math problems and quickly give in to the notion that they will never use math in “real life” situations. While it may be true that some of the more abstract mathematical concepts rarely come into play, the underlying skills developed in high school math classrooms resonate throughout a student’s lifetime and often resurface to help solve various real world or work-related problems sometimes years down the line.

1. Ask any contractor or construction worker and they’ll tell you just how important math is when it comes to building anything. Creating something that will last and add value to your home out of raw materials requires creativity, the right set of tools, and a broad range of mathematics.

   

    Figuring the total amount of bags of concrete needed for a slab, accurately measuring lengths,       widths, and angles, and estimating project costs are just a few of the many cases in which math is necessary in real life home improvement projects.

2.One of the more obvious places to find people using math in everyday life is at your neighborhood grocery store. Grocery shopping requires a broad range of math knowledge from multiplication to estimation and percentages.
Calculating price per unit, weighing produce, figuring percentage discounts, and estimating the final price are all great ways to include the whole family in the shopping experience.

Encourage your students to play math challenges at the grocery store with their family by attempting to estimate the total cost of all groceries prior to checkout. The difficulty can be increased by incorporating coupons, sales, and adjusted pricing for bulk items. Your little bargain shoppers will thank you later when they’re saving money on their own groceries.

3.

More math can be found in the kitchen than anywhere else in the house. Cooking and baking are sciences all their own and can be some of the most rewarding (and delicious) ways of introducing children to mathematics. After all, recipes are really just mathematical algorithms or self-contained step-by-step sets of operations to be performed.

The proof is in the pudding!

Working in the kitchen requires a wide range of mathematical knowledge, including but not limited to:

• measuring ingredients to follow a recipe
• multiplying / dividing fractions to account for more or less than a single batch
• converting a recipe from Celsius to Fahrenheit
• converting a recipe from metric (mL) to US standard units (teaspoon, tablespoon, cups)
• calculating cooking time per each item and adjusting accordingly
• calculating pounds per hour of required cooking time
• understanding ratios and proportions, particularly in baking (ex. the recipe calls for 1 egg and 2 cups of flour, then the ratio of eggs to flour is 1:2).

Following a recipe can sometimes be tricky, especially if conversions are necessary. We Americans follow our own set of rules when it comes to most forms of measurement. Conversions make it a bit more difficult to follow recipes from other countries as they most likely use Celsius and the metric system.
  Taken from https://www.thinkthroughmath.com/math-real-life-examples/

Indian Mathematicians

Srinivasa Ramanujan

Srinivasa Ramanujan is one of the celebrated Indian mathematicians. His important contributions to the field include Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan’s identities in partition of numbers, work on algebra of inequalities, elliptic functions, continued fractions, partial sums and products of hypergeometric series.

C.R. Rao
Calyampudi Radhakrishna Rao, popularly known as C R Rao is a well known statistician, famous for his “theory of estimation”.

D. R. Kaprekar

D. R. Kaprekar discovered several results in number theory, including a class of numbers and a constant named after him. Without any formal mathematical education he published extensively and was very well known in recreational mathematics cricle

taken from

famous.mathematicians.com

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Indian Mathematicians

It is no doubt that the world today is greatly indebted to the contributions made by Indian mathematicians. One of the most important contribution made by them was the introduction of decimal system as well as the invention of zero. Here are some the famous Indian mathematicians dating back from Indus Valley civilization and Vedas to Modern times.
Aryabhata

Aryabhata worked on the place value system using letters to signify numbers and stating qualities. He discovered the position of nine planets and stated that these planets revolve around the sun. He also stated the correct number of days in a year that is 365.

Brahmagupta
The most significant contribution of Brahmagupta was the introduction of zero(0) to the mathematics which stood for “nothing”.

taken from

http://www.famous-mathematicians.com/top-10-indian-mathematicians-contributions/

Inspiring Mathematicians

Leonhard Euler (1707- 1783)
The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula eiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He later took an interest in Latin squares – grids where each row and column contains each member of a set of numbers or objects once. Without this work, we might not have had sudoku.

Carl Friedrich Gauss (1777-1855)

Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death. During his analysis of astronomical data, he realised that measurement error produced a bell curve – and that shape is now known as a Gaussian distribution.

taken from

https://www.theguardian.com/culture/2010/apr/11/the-10-best-mathematicians

Can you find the answer?

Inspiring Mathematicians

Pythagoras (circa 570-495BC)

Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat beans.

Girolamo Cardano (1501 -1576)

Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty

Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers. This was a revolutionary idea, and it led to probability theory, which in turn led to the birth of statistics, marketing, the insurance industry and the weather forecast.

Taken from......

https://www.theguardian.com/culture/2010/apr/11/the-10-best-mathematicians

World Maths Day:

20 Interesting and Amazing Facts

About Maths Posted By: Ambika Updated: Thursday, October 15, 2015, 13:03 [IST]

                     Words such as formula, equation and calculation sounds boring for those who hate Maths as a subject, whereas it is fun for those who have keen interest towards solving equations/problems.October 14th is celebrated as World Maths Day. Let us know some interesting and amazing facts about Mathematics.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.

2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion

3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D

4. 2 and 5 are the only primes that end in 2 or 5

5. An icosagon is a shape with 20 sides

6. Among all shapes with the same perimeter a circle has the largest area.

7. Among all shapes with the same area circle has the shortest perimeter

8. 40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order

9. 'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself

10. From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand")

11. 12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

12. Have you ever noticed that the opposite sides a die always add up to seven (7)

13. Trigonometry is the study of the relationship between the angles of triangles and their sides

14. Abacus is considered the origin of the calculator

15. Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3)

16. Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).

17. If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050

18. A 'jiffy' is an actual unit of time for 1/100th of a second

19. Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421

20. Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on

Read more at: https://www.careerindia.com/news/20-interesting-amazing-facts-about-maths-015921.html

SPEED MULTIPLYING WITH 21, 31, 41........

To multiply by 21:   Double the number, then multiply by 10, and add the original number.

for example,  to multiply 42 by 21,

      Double 42 yields 84,  when we multiply it with 10 we get 840, and then add the original number 42 we get 882.

To multiply with 31:  Triple the number, then multiply with 10, and add the original number.

For example, to multiply 17 by 31,

       triple of 17 is 51, multiplying 41 by 10 we get 510, and we get 527 when we add 17- the original number with 510.  

To multiply by 41: Quadruple the number, then multiply by 10, and add the original number          

very useful in practical life which I found in the 8th standard text book.....

• Find the area of the coloured region.

SOLUTION:

Given:        radius of the quadrant of a circle =  3 cm

                   Length of the rectangle               = 15 cm

                   Breadth of the rectangle              =  8  cm

to find:       Area of the coloured region        = Area of the rectangle - area of the four quadrants    of

                                                                                                                a circle

                                                                       

                                                                       = b × h sq.units  -  4 × (1/4 ×πr² )   

                                                                       = (15×8)   - (22/7 × 3 × 3)

                                                                       = 120 -28.29

                                                                       = 91.714 cm ²

^{Area of the coloured region =} 91.714 cm ²

Nice to know...............

https://www.google.co.in/

participation in blogging community

Maths puzzles

Maths puzzles

Magic square

Amazing facts but interesting........

Is it Magic or Is it Maths?

Stage: 3  

Here are three 'tricks' to amaze your friends.

But the really clever trick is explaining to them why these 'tricks' are maths and not magic. Like all good magicians, you should practise by trying them. Can you explain how they work?

This trick will impress even your maths teacher.

• Think of a number.
• Double it.
• Add 10.
• Halve it.
• Take away you original number.
• Is your answer 5?

Try this with a different starting number. Did you get a different result? Why does this happen?
Write the answer on a piece of paper without letting anybody see it and seal it in an envelope. Have somebody hold the envelope and at the end ask them to open it and reveal the number you wrote at the beginning. Wow, Magic!

https://nrich.maths.org/1051

BY BEN RANKIN

http://www.mirror.co.uk/news/weird-news/amaze-your-friends-with-these-fantastic-maths-1593633

fantastic maths magic tricks

One, two, three

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

http://www.mirror.co.uk/news/weird-news/amaze-your-friends-with-these-fantastic-maths-1593633

Fantastic maths magic tricks

Threesy does it

You can discover whether a number is a multiple of 3 just by checking whether this is true for the sum of its digits.

For example, 12,894 has 1 + 2 + 8 + 9 + 4 = 24 = 3 x 8, so 12,894 is a multiple of 3.

You don't need to do the long division in order to find this out.

You can do this even for huge numbers that your calculator could never cope with.

For example, try: 111,222,333,444,555,666,777, 888,987. Is it divisible by 3? In fact, if you're clever, you might be able to give the answer before summing the digits.

10% up then 10% down means you lose out

A worker's boss explains that in order to stay competitive he will have to cut his pay by 10% but he will allow the employee to work 10% more hours to make up for it, "so your pay will be maintained".

Afraid not! If the worker was being paid, say, £100, the 10% cut takes him down to £90. The 10% extra hours will add back on 10% of £90, which gives him £99. He is still £1 worse off. Beware percentages - you need to know what they refer to.

Never-ending squares

Square numbers (the products of numbers multiplied by themselves) and prime numbers are important and your internet security only works because the prime numbers never run out.

You can get the endless list of squares just by adding the odd numbers up: 1 = 1 x 1, 1 + 3 = 4 = 2 x 2, 1 + 3 + 5 = 9 = 3 x 3, 1 + 3 + 5 + 7 = 16 = 4 x 4 ... and this pattern never lets you down.

However, when it comes to primes, we still have to go out hunting for them, which is why at any one time there is always a world champion largest known prime.

'Mind reading' trick

Choose a single-digit number, multiply it by 9 and if the answer has two digits add them together.

Subtract 5 from what you have, giving you a number. Turn the number into a letter by the rule A = 1, B = 2 and so on. Think of a country beginning with your letter. Take the last letter of your country and think of an animal that begins with that letter. It's odds on that you have a kangaroo in Denmark.

It all adds up... to 9

1x9=09 =0+9=9

2x9=18 =1+8=9

3x9=27 =2+7=9

4x9=36 =3+6=9

5x9=45 =4+5=9

6x9=54 =5+4=9

7x9=63 =6+3=9

8x9=72 =7+2=9

10 x 9 = 90 = 9 + 0 = 9

maths magic

http://www.mirror.co.uk/news/weird-news/amaze-your-friends-with-these-fantastic-maths-1593633

Maths Magic

Twos, threes & fives

Think of a number. Add 4, then multiply the result by 4. Subtract 8, then divide the result by 4. Finally take away your original secret number. The answer is 2.

Think of another number.

Double it. Add 9. Subtract 3. Divide by 2. Subtract your original number. The answer is 3.

Think of any three-digit number.

Add 7. Multiply by 2.

Subtract 4, then divide the result by 2.

Subtract it from the original number you thought of.

The answer is 5.

Ninety nine

Write down any two different numbers from 1 to 9. Then reverse the two numbers.

You should have two two-digit numbers.

Subtract the smaller number from the larger one.

Take the result, reverse the digits, and add that number to the one you got when you subtracted.

The answer is 99.

For example: 72 reverses to make 27.

Subtract the smaller (27) from the larger (72): 45.

Reverse these digits to make 54.

Add this to the previous number.

The answer is 99.