Physics Question
Finally, your friend's twin engine jet airplane lands. As it stands on the runway, you hear the sound of the engines getting louder and softer, rhythmically once every 2.3 s. The average frequency you hear is 3650 Hz. What are the differences between the average frequency and the individual frequencies of the sounds from each engine?
frequency you hear is 3650 Hz. What are the differences between the average frequency and the individual frequencies of the sounds from each engine?
flow - favg = ______ Hz
HELP: The rhythmic getting louder and softer that you hear is the phenomenon of beats.
HELP: What is the beat frequency in this case? What is the relationship between the beat frequency and the two frequencies that generate the beats?
HELP: What is the relationship between those two frequencies and the average frequency you hear?
fhigh - favg = ______ Hz
I've tried a couple of things but I'm just stumped! Thanks for the help.
That is definitely not the answer
To find the differences between the average frequency and the individual frequencies of the sounds from each engine, we can use the concept of beats. Beats occur when two sound waves of slightly different frequencies interfere with each other.
Let's denote the frequency of the first engine's sound as f1 and the frequency of the second engine's sound as f2. The average frequency you hear, which is 3650 Hz, is given by favg.
The beat frequency (flow) is the frequency at which the loudness of the sound appears to fluctuate. In this case, the beat frequency is 1/2.3 Hz, or approximately 0.4348 Hz, as the beats occur once every 2.3 seconds.
The beat frequency is equal to the absolute difference between the frequencies of the two engine sounds. So,
flow = |f1 - f2|
We can rearrange this equation to solve for either f1 or f2:
f1 = f2 + flow
Now, we know that the average frequency you hear (favg) is the average of the individual engine frequencies:
favg = (f1 + f2) / 2
We can use this equation to solve for the difference between the average frequency and the individual frequencies:
f1 - favg = f1 - (f1 + f2) / 2
= (2f1 - f1 - f2) / 2
= (f1 - f2) / 2
Therefore, the difference between the average frequency and the frequency of each engine sound is (f1 - f2) / 2.
Substituting the beat frequency (flow) for (f1 - f2), we have:
flow = (f1 - f2) / 2
Solving for f2:
f2 = f1 - 2flow
Now we can substitute this value of f2 back into the equation for the difference between the average frequency and the individual frequencies:
fhigh - favg = (f1 - 2flow) - ((f1 + f2) / 2)
= (f1 - 2flow - f1 - f2) / 2
= (-f2 - 2flow) / 2
= -(f2 + 2flow) / 2
= -(f2 + 2favg)
Therefore, the difference between the average frequency and the frequency of each engine sound is -(f2 + 2favg).
By substituting the given values of favg and flow, you should be able to calculate the actual numerical differences between these frequencies.