A tape recorder playing a single tone of frequency f_{0} is dropped from rest at a height h. You stand directly underneath the tape recorder and measure the frequency observed as a function of time. Here t=0 \mathrm{~s} is the time at which the tape recorder was dropped.
| t(\mathrm{~s}) | f(\mathrm{~Hz}) |
|---|---|
| 2.0 | 581 |
| 4.0 | 619 |
| 6.0 | 665 |
| 8.0 | 723 |
| 10.0 | 801 |
The acceleration due to gravity is g=9.80 \mathrm{~m} / \mathrm{s}^{2} and the speed of sound in air is v_{\text {snd }}=340 \mathrm{~m} / \mathrm{s}. Ignore air resistance. You might need to use the Doppler shift formula for co-linear motion of sources and observers in still air,
where f_{0} is the emitted frequency as determined by the source, f is the frequency as detected by the observer, and v_{\text {snd }}, v_{\text {src }}, and v_{\text {obs }} are the speed of sound in air, the speed of the source, and the speed of the observer. The positive and negative signs are dependent upon the relative directions of the motions of the source and the observer.
a. Determine the frequency measured on the ground at time t, in terms of f_{0}, g, h, and v_{\text {snd }}. Consider only the case where the falling tape recorder doesn’t exceed the speed of sound v_{\text {snd }}.
b. Verify graphically that your result is consistent with the provided data.
c. What (numerically) is the frequency played by the tape recorder?
d. From what height h was the tape recorder dropped?