Your clock radio awakens you with a steady and irritating sound of frequency 600 Hz. On morning, it malfunction and cannot be turned off. In frustration, you drop the clock radio out of your fourth-story dorm wndow 15.0m from the ground. Assume the speed of sound is 343 m/s. As you listen to the falling clock radio, what frequency do you hear just before you hear it striking the ground?

Explanation

The speed of clock radio increases as it falls. Therefore, it is a source of sound moving away from you with an increasing speed, so the frequency you hear should be less than 600 Hz. We categorize this problem as one is which we must combine our understanding of falling objects with that of the frequency shift due to Doppler effect. Because the clock radio is modelled as a particle under constant acceleration due to gravity the speed of the source of sound is
`v_S="gt"`
Now to determine the Doppler-shifted frequency heard from the falling clock radio, We have
`f'=((v)/(v+v_S))f=((v)/(v+"gt"))f` .(i)
Find the time at which the clock radio strikes the ground.
`implies-15.0m=00+0-(1)/(2)(9.80(m)/(s^2))t^2`
`impliest=1.75s`
From Eq. (i) evaluate the Doppler-shifted frequency just as the clock radio strikes the ground.
`f'=[((343(m)/(s)))/(343(m)/(s)+(9.80(m)/(s^2))(1.75s))](600Hz)=571Hz`
The frequency is lower than the actual frequency of 600 Hz because the clock radio is moving away from you. If it were to fall from a higher floor so that it passes below `y=-15.0m`, The clock radio would countinue to accelerate and the frequency would continue to drop.