You set a tuning fork into vibration at a frequency of 763 Hz and then drop it o

Question

You set a tuning fork into vibration at a frequency of 763 Hz and then drop it off the roof of the Physics building where the acceleration due to gravity is 9.80 m/s2. Determine how far the tuning fork has fallen when waves of frequency 733 Hz reach the release point? (Take the speed of sound in air to be 343 m/s.)

I tried to look at similar problems with different numbers but did not get the right answer. I got the following feedback: "How is the frequency heard by the observer related to the frequency of the source when the source is moving away from the observer? How is the speed of the source related to how far it has fallen? Is it necessary to take into consideration the distance the tuning fork travels, while the sound is traveling from the source to the release point?"

Explanation / Answer

use distance travelled S = 0.5 gt^2

here t ime period t = 1/f

t = 1/(763)

t = 0.00131 secs

so

distance travelled S = 0.5 * 9.8 * 0.00131 * 0.00131

S =   8.4 um

--------------------------------
use the equation of Doppler effect as

when source is moving away

fo = fs *(V+Vs)/(V+Vo)

where fs is the frequency of source

V is the speed of sound = 340 m/s

Vs is the speed of soruce

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