You set a tuning fork into vibration at a frequency of 723 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 697 Hz reach the release point?

This question involves the concepts of doppler's effect and the equations of motion.

The tuning fork has fallen by a height of "8.36 m".

From Doppler's Effect we have:

where,

= apparent frequency of sound waves = 697 Hz

= actual frequency of sound waves = 723 Hz

v = speed of sound = 343 m/s

= speed of observer = 0 m/s

= speed of source = ?

Therefore,

Now, we will use the third equation of motion to find out the height fell by the tuning fork:

where,

g = acceleration due to gravity = 9.8 m/s²

h = height fell = ?

vf = final speed of tuning fork = v_s = 12.8 m/s

vi = initial speed of tuning fork = 0 m/s

Therefore,

h = 8.36 m

Learn more about equations of motion here:

link

The attached picture shows the equations of motion.

Explanation:

Given

Original Frequency

apparent Frequency

There is change in frequency whenever source move relative to the observer.

From Doppler effect we can write as

where  

apparent frequency  

v=velocity of sound in the given media

velocity of source

velocity of observer  

here

i.e.fork acquired a velocity of

distance traveled by fork is given by

where v=final velocity

u=initial velocity

a=acceleration

s=displacement