LEND ME YOUR EAR, I WILL TELLYOUR AGE

If a bell is stroked in a place of worship, it vibrates; set the air molecules in vibration; molecules strike eardrum and vibrates it; our brain interprets the vibrations and we perceive the sound. We understand that the vibrations are the basis for the sound. Number of vibrations taking place in one second is called "frequency". Suppose there are 100 vibrations per second, we say, the frequency is 100 hertz or 100 Hz.

    The human ears are extremely sensitive to the frequency range 2000 hz -5000 hz.  All humans at any age can hear up to 8000 hz clearly.  Persons of age over 50, cannot hear 12000 hz.
Over 40 - can hear up to 15000hz
over 30- up to 16000hz
above 17 khz, even young persons under 25 age, struggle to hear that frequency.  Only newborn may hear them.
    Why does our hearing appear to 'age'.  Our ears have distinctive, spiral-shaped part called the cochlea and it is filled with fluids and tiny hairs called cilia.  These cilia are vibrated by air molecules (sound waves) and we sense the sound.  The most sensitive cilia get destroyed as we age.
    The cilia do not regrow.  Loud music from headphones is harmful. So, do not raise the volume beyond allowed level.
     Many animals can hear higher frequencies.

Dog- 64hz -44khz
Mouse- 900hz-79khz
cat-55hz -77khz
dolphin -150hz –150khz

    We, humans can hear up to 8 k hz comfortably, but dolphin can hear up to 150khz.
    The sound waves which have frequencies more than 20 khz (that we cannot hear) is called ultrasonic waves.  Many medical instruments use ultrasonic waves for scanning purpose.

NOTE: 1. When you go near an electrical transformer, you hear a humming sound. The frequency of electric current is 50 hz and that is also the frequency of humming noise.
Note 2. All objects like wine glass, bell, table, plate, wall etc. have their own natural frequency.
Note 3. As we age, our vision, hearing, taste, muscle strength may get eroded. Our teeth, hair may fall, but our determination, thoughts, mind, enthusiasm should remain young and strong as ever.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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