Two identical tuning forks have frequencies of 512 Hz. If one is held by a listener while the other approaches at a speed of 7.2 m/s, what does the listener hear?
To find what the listener hears when one tuning fork approaches at a certain speed, we can use the Doppler effect formula.
The Doppler effect describes the change in frequency of a wave (sound wave, in this case) due to the relative motion between the source of the wave and the observer.
The formula for the Doppler effect is:
f' = f * (v + v₀) / (v + v₀₂)
Where:
f' is the observed frequency
f is the actual frequency of the source
v is the speed of sound in the medium (which we assume to be constant)
v₀ is the speed of the observer
v₀₂ is the speed of the source
Given:
f = 512 Hz (frequency of the tuning fork)
v₀ = 0 m/s (the listener is holding one tuning fork)
v₀₂ = 7.2 m/s (the other tuning fork is approaching at a speed of 7.2 m/s)
Since the two tuning forks are identical, their actual frequencies are the same.
Plugging the values into the formula, we have:
f' = 512 * (v + 0) / (v + 7.2)
Now, to find what the listener hears, we need to know the speed of sound in the medium, which is typically around 343 m/s in air at room temperature.
So, substituting v = 343 m/s into the formula, we get:
f' = 512 * (343 + 0) / (343 + 7.2)
Calculating this expression will give us the observed frequency f'.