Question

Chanukya was eager to know the time taken by sound to travel the same distance in water and air. So, he set a body on vibration with a frequency of 250 Hz in air and the sound produced bu this is heard at a distance of 175 m. Now if the body is vibrated in water, what is the difference in the time taken by the sound to travel the same distance in water and air ?
(The velocity of sound in air and water is `350 ms^(-1)` and `1400 ms^(-1)`, respectively).

Answer 1

(i) Frequency of body, (n) = 250 Hz.
Distance, (d) = 175 m.
Speed (velocity) of sound (V) `= 350 ms^(-1)`.
`therefore` Time taken by the sound to travel 175 m in air `= ("distance")/("speed") = (175 m)/(350 ms^(-1)) = 1/2 s.`
(ii) When it is vibrated in water, the number of vibrations completed in 1 second (i.e., frequency) is the same
`therefore` n = 250 Hz.
Distance, (d) = 175 m
Speed of sound in water `(v) = 1400 ms^(-1)`.
`therefore` Time taken by sound to travel 175 m in water (t).
`= (175 m)/(1400 ms^(-1)) = 1//8 s`
`therefore` Time difference `= (1/2 - 1/8)s`
`= (1/2 - 1/8)s = (4/8 - 1/8)s = 3/8s`.