In order to be able to determine her speed, a skydiver carries a tone generator.

Question

In order to be able to determine her speed, a skydiver carries a tone generator. A friend on the ground at the landing site has equipment for receiving and analyzing sound waves. While the skydiver is falling at terminal speed, her tone generator emits a steady tone of 1480 Hz. Assume: The air is calm and that the sound speed is 343 m/s, independent of altitude. If her friend on the ground (directly beneath the skydiver) receives waves of frequency 3260 Hz, what is the skydiver's speed of descent? Answer in units of m/s. If the skydiver were also carrying sound-receiving equipment sensitive enough to detect waves reflected from the ground, what frequency would she receive? Answer in units of Hz.

Explanation / Answer

Since the diver, who is the source of the sound waves, is moving towards her friend on the ground, who is the receiver of the waves, the Doppler formula takes the form fg=fe(v/(v-vdiver)) so, 1-(vdiver/v)=fe/fg Solving for vdiver, we have vdiver=v(1-fe/fg) =343m/s(1-(1480/3260)) =188.65 m/s If the waves are reflected, and the skydiver is moving towards them, we have frec=fg[(v+vdiver)/v] =(3260 Hz)*[343m/s+188.65m/s]/343m/s =5053 Hz

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