Question

1. A skydiver carries a buzzer which emits a steady 1800 Hz tone. A friend on the ground (directly below the skydiver) listens to the doppler shifted frequency. Assume the air is calm and that the speed of sound is independent of altitude. While the skydiver is falling at terminal velocity (the constant speed reached due to the balance of the downward gravitational force and the upward drag force due to air resistance), her friend on the ground hears waves of frequency 2150 Hz. a. How fast is the skydiver falling

Answer 1

vs = 55.84 m/s

Step-by-step explanation:

In this case, the source (skydiver with buzzer) is moving towards the observer (friend). The formula for this case will be:

`f' = (v)/(v-v_s) f`

where,

f' = shifted frequency = 2150 Hz

f = actual frequency = 1800 Hz

v = speed of sound = 343 m/s

vs = speed of skydiver = ?

Therefore,

`2150\ Hz = (343\ m/s)/(343\ m/s - v_s)(1800\ Hz)\\\\343\ m/s - v_s = (343\ m/s)/(2150\ Hz) (1800\ Hz)\\\\v_s = 343\ m/s - 287.16\ m/s\\`

vs = 55.84 m/s