You are sitting on a train that is about to drive into a tunnel that is at the base of a large cliff. Just before entering the tunnel, the train blows its whistle, which has a frequency of 600 Hz. (a) What frequency do you hear from the whistle directly? (b) What frequency does a stationary person who is ahead of the train hear? (c) What frequency does a stationary person who is behind the train hear? (d) What frequency do you hear in the echo off of the cliff?
for A I was pretty sure that it would be 600 Hz because neither the train and I am moving. But for the other ones I was confused because I dont know how far the stationary person ahead of the train is or behind
without knowing the speed of the train, there are no exact answers for b, c, and d
you are correct for a
b will hear a higher frequency
c will hear a lower frequency
d will hear the highest frequency
... the train (whistle) is moving toward the cliff, so the echo will be a higher frequency
... you are moving toward the cliff (source) so the echo frequency is even higher ... double doppler shift
To answer these questions, we need to consider the concept of the Doppler effect, which explains the change in frequency of a sound wave due to relative motion between the source of the sound and the observer.
(a) What frequency do you hear from the whistle directly?
Since you and the train are not moving, the frequency you hear would be the same as the frequency of the whistle, which is 600 Hz. So you are correct.
(b) What frequency does a stationary person who is ahead of the train hear?
If a person is stationary and ahead of the train, the train is moving closer to them. As the train moves closer to the person, the frequency of the sound waves appears higher to the person, resulting in a higher perceived frequency. This effect is known as the "blue-shift" in sound. To calculate the perceived frequency, we can use the formula:
f’ = f * (v + v₀) / (v + v_s)
Where:
f’ is the perceived frequency
f is the actual frequency of the whistle (600 Hz)
v is the speed of sound (343 m/s)
v₀ is your velocity (assuming you and the train are not moving)
v_s is the velocity of the stationary person (towards the train)
However, we need to know the velocity of the stationary person (v_s) towards the train to get an exact answer. Without that information, we cannot determine the exact frequency the person would hear. But, we can say that the frequency would be higher than 600 Hz.
(c) What frequency does a stationary person who is behind the train hear?
If a person is stationary and behind the train, the train is moving away from them. As the train moves away, the frequency of the sound waves appears lower to the person, resulting in a lower perceived frequency. This effect is known as the "red-shift" in sound. Using the same formula as before, we can calculate the perceived frequency, but this time with the velocity of the stationary person (v_s) being away from the train. Again, without the knowledge of v_s, an exact frequency cannot be determined, but the perceived frequency would be lower than 600 Hz.
(d) What frequency do you hear in the echo off of the cliff?
When the sound wave reaches the cliff, it reflects or echoes back towards you. This reflected sound will have the same frequency as the original sound wave. Therefore, the frequency you hear in the echo off of the cliff would also be 600 Hz.