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 determine what the listener hears, we need to consider the concept of the Doppler effect. The Doppler effect is the change in frequency of a wave (such as sound or light) that occurs when the source of the wave is moving relative to the observer.
In this case, one of the tuning forks is approaching the listener at a certain speed. The frequency heard by the listener will depend on whether the source is moving towards or away from the listener.
When a sound source is moving towards an observer, the frequency of the sound waves is perceived as higher (a higher pitch). Conversely, when a sound source is moving away from an observer, the frequency is perceived as lower (a lower pitch).
Given that the tuning forks are identical, with frequencies of 512 Hz each, we need to consider the relative motion between the forks and the listener.
If the tuning fork approaches the listener, the frequency perceived will be higher. If it moves away from the listener, the frequency perceived will be lower. The actual change in frequency can be calculated using the equation:
f' = f((v+vr)/(v-vs))
Where:
f' is the perceived frequency
f is the actual frequency emitted by the source
v is the speed of sound (which is approximately 343 m/s at room temperature)
vr is the velocity of the receiver (listener)
vs is the velocity of the source (the tuning fork)
In this case, the tuning fork is approaching the listener at a speed of 7.2 m/s. Since the velocity of sound is constant, we can assume v remains as 343 m/s.
Let's calculate the perceived frequency using the formula:
f' = 512 Hz * ((343 m/s + 7.2 m/s) / 343 m/s)
Simplifying the equation:
f' = 512 Hz * (350.2 m/s / 343 m/s)
= 524.4 Hz
Therefore, the listener would hear a frequency of approximately 524.4 Hz when one of the tuning forks approaches at a speed of 7.2 m/s.