The Mysterious Case of the Falling Tuning Fork

How far has the tuning fork fallen when the student hears a frequency of 400 Hz?

Can you calculate the distance the tuning fork has fallen down the elevator shaft?

Calculating the Distance the Tuning Fork Has Fallen

When the physics student drops a vibrating 440-Hz tuning fork down the shaft and hears a frequency of 400 Hz, we can use the Doppler effect formula to determine the distance the tuning fork has fallen.

The Doppler effect, also known as the Doppler shift, explains changes in frequency caused by moving sources of sound with regard to an observer. As the source gets closer to the observer, the waves become compressed and the frequency increases.

The mathematical formula for the Doppler effect is:

f₀ = ((v + v₀) / (v + v_s)) * f_s

By plugging in the given values, we can calculate the velocity of the tuning fork as 34.5 m/s. Then, using the formula for distance fallen under gravity:

(v_fork * t²) / 2 = (34.5 * 2) / 19.6

Therefore, the tuning fork has fallen a distance of 3.52 meters down the elevator shaft.