# Illustrations

Determine the value of *g* if a simple pendulum of length 1 m has a time period of 2 s.

Given: *L* = 1 m, *T* = 2 s, *g* = ?

*g* = (3.14)^{2} = 9.8596 m s^{â€“2}.

A simple pendulum has a time period of 2 s on the earthâ€™s surface. It is taken to a height *R _{e}* above the earthâ€™s surface, where

*R*is the radius of the earth. Find the time period at that height.

_{e}Let the acceleration due to gravity be *g* at the earthâ€™s surface and *g*Â´ at the said height. At that height, the distance of the pendulum from earthâ€™s centre is *R _{e }*+

*R*= 2

_{e}*R*.

_{e}We know that [here *M _{e}* is the mass of the earth]

(1)

The time period of the pendulum at the earthâ€™s surface

(2)

The time period at the height *R _{e}* is

(3)

Dividing (3) by (2), we get

Therefore, The time period at height *R _{e}* is 4 s.

Calculate the wavelength of the wave generated by a tuning fork of frequency 256 Hz. The velocity of sound in air at ordinary conditions is 340 m s^{â€“1}.

Given, *f* = 256 Hz, *v* = 340 m s^{â€“1}

Since, *v* = *f *Î»

The wavelength and frequency of a sound wave in a certain medium is 40 cm and 825 Hz, respectively. In the same medium, if another wave has the wavelength equal to 32 cm, calculate its frequency.

Given, Î» = 40 cm = 0.40 m, *f* = 825 Hz

*v* = *f* Î» = 825 Ã— 0.40 = 330 m s^{â€“1}.

In the second case, since medium is the same, the velocity of sound will remain the same.

Now, *v* = 330 m s^{â€“1}, Î» = 32 cm = 0.32 m

From *v* = *f *Î»

A man standing on a terrace hears a thunder. The time interval between a lightning flash and first clap of thunder was found to be 15 s. Calculate the distance of the flash from the observer (speed of sound in air is 332 m s^{â€“1}).

Since the speed of light is very high, we can assume that the lightning flash is seen at the same instant as it is generated.

Time interval *t* = 15 s

Speed of sound *v* = 332 m s^{â€“1}

Let *d* be the distance covered by the sound waves. Then,

Therefore, the distance of the observer from the flash is 4980 m.

A stone is dropped into a well 44.1 m deep. The sound of the splash is heard 3.13 s after the stone is dropped. Find the velocity of sound in air. [Take *g* = 9.8 m s^{â€“2}]

For vertically downward motion of the stone:

Initial velocity *u* = 0 (being dropped)

Acceleration due to gravity *g* = 9.8 m s^{â€“2}

Distance covered *h* = 44.1 m

Time taken *t* = ?

We have

( â€¦ *u* = 0)

Time taken by the sound from the splash to travel from water surface to the edge of the well is 3.13 â€“ 3 = 0.13 s.

For upward motion of the sound waves in air

Therefore, velocity of sound in air is 339.23 m s^{â€“1}.