Question

Q-1) A body vibrating with a time period of 1/256s produces a sound wave which travels in air with a velocity of 350 m/s . Calculate the wavelength .

Q-2)A worker lives at a distance of 1.32 km from the factory .If the speed of sound in air be 330m/s ,how much time will the sound of factory siren take to reach the worker.

Q-3) The flash of a gun is seen by a man 3 seconds before the sound is heard . Calculate the distance of the gun from the man (speed of sound in air is 332 m/s ).

Q-4)The echo of a sound is heard after 5 seconds .If the speed of sound in air be 342m/s.calcualte the distance of the reflecting surface.

*Please give correct ans

Answer 1

i. the wavelength is 1.3671875
ii.time taken is 4 sec
iii. distance is 996m
iv. distance of reflecting surface is 855m

Answer 2

SOLUTIONS

A-1) Time period =
$\frac{1}{256} seconds$
Frequency = 256 Hz
Velocity of sound waves =
$wavelength \times frequency$
350 =
$wavelength \times 256$
Therefore, Wavelength =
$\frac{350}{256} = 1.37m$
Hence, Wavelength of the sound wave is 1.37 m.
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A-2) Distance between the worker's house and the source of sound = 1.32 km=1320 m

Speed of sound = 330m
Speed = Distance /Time taken
Time taken = Distance /Speed
= 1320/330
= 4 secs
Therefore, the sound of the factory siren will take 4 seconds to reach the worker.
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A-3)Let the time at which the flash is seen be t.
Time at which the sound is heard = t + 3 
Distance traveled by light wave = Distance traveled by sound wave
3 X 10 *8 X t = 332 X (t + 3)
3 X 10 *8 X t = 332 t + 332 x 3
3 X 10 *8 X t = 332 t + 996
3 X 10 *8 X t - 332 t = 996
Since the value of 332 is almost negligible as compared to 3 X 10*8 therefore the above equation can be rewritten as 
3 X 10 *8 X t = 996
or
t =996/3 X 10 *8 

Distance of the gun from the observer = speed of light X time taken
= 3 X 10*8 X 996 /3 X 10*8 
= 996 meters
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A-4) If d is the distance of reflecting surface from the source and t is the time interval of echo-return, then

2d = vt => d= vt/2

Here,
$v = 343ms { }^{ - 1} \: and \: t = 3s \\ therefore \: d = \frac{343 \times 3}{2} = 513 \: m$