A speaker which produces a frequency of 400 Hz is moving away from an observer and towards a wall at 5 m/s when it is 23 degrees Celsius. What is the frequency of the sound that travels back to the observer? What is the frequency of the sound that travels forward and bounces off the wall, then gets to the observer?
and your thinking is?
My thinking is:
f2=f1(V/V+Vs)
f2=Heard frequency=394.3 Hz
f1=Source frequency=400Hz
V=velocity of sound in medium=332+0.6(23)=345.8 m/s
Vs=velocity of source=5 m/s
I'm not sure about the second question, though.
The wall will send back exactly the frequency it hears, because it is stationary.
It will hear a higher frequency than is radiated because the source is moving toward the wall.
So the answer to the first question is 394.3 Hz and the answer to the second question is 400 Hz?
Yes, on the first. But the second, the speaker is moving toward the wall, so it is an upward doppler pitch, and that exact frequency is reflected.
So the answer is 400(345.8/340.8) = 405.87 Hz?
To determine the frequency of the sound that travels back to the observer as well as the frequency of the sound that travels forward, bounces off the wall, and then reaches the observer, we can use the Doppler effect equation.
The Doppler effect describes the change in frequency of a wave (in this case, sound) due to the relative motion between the wave source (the moving speaker) and the observer (you).
The Doppler effect equation is given by:
f' = ((v + vo) / (v - vs)) * f
where:
f' is the observed frequency
v is the speed of sound in air
vo is the velocity of the observer with respect to the medium (positive if moving towards the source, negative if moving away)
vs is the velocity of the source with respect to the medium (positive if moving away from the observer, negative if moving towards)
f is the frequency of the source
Now let's calculate the frequency for both scenarios.
1. Frequency of the sound that travels back to the observer:
In this case, the observer is stationary, so the velocity of the observer (vo) is 0 m/s. The speaker is moving away from the observer, so the velocity of the source (vs) is 5 m/s.
Plugging these values into the Doppler effect equation, we get:
f' = ((v + vo) / (v - vs)) * f
f' = ((v + 0) / (v - 5)) * 400 Hz
2. Frequency of the sound that travels forward, bounces off the wall, and reaches the observer:
In this case, the observer is stationary, so the velocity of the observer (vo) is 0 m/s. The speaker is also moving towards the wall, so the velocity of the source (vs) is -5 m/s (negative indicating motion towards the observer).
Plugging these values into the Doppler effect equation gives us:
f' = ((v + vo) / (v - vs)) * f
f' = ((v + 0) / (v - (-5))) * 400 Hz
Remember that we also need to know the speed of sound in air, but it is not given in the question. The speed of sound in air is approximately 343 meters per second at 23 degrees Celsius. You can plug this value into the equations to calculate the specific frequencies for both scenarios.