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?

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?

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

Answer 1

To find the differences between the average frequency and the individual frequencies of the sounds from each engine, we need to understand the concept of beats.

Beats occur when two sounds of slightly different frequencies interfere with each other. The result is a pattern of alternating louder and softer sounds. The beat frequency is the number of times these loud-soft patterns occur per second.

In this case, the beat frequency is given as once every 2.3 seconds, which means that the time it takes for one beat is 2.3 seconds. We can find the beat frequency by taking the reciprocal of this time:

Beat frequency = 1 / Time for one beat = 1 / 2.3 Hz = 0.4348 Hz.

The beat frequency is the difference between the frequencies of the two sounds that generate the beats. Therefore, we have:

Beat frequency = |f1 - f2|,

where f1 and f2 are the frequencies of the sounds from the first and second engines, respectively.

Next, we can relate the beat frequency to the average frequency we hear:

Beat frequency = |f1 - f2| = (favg - f1) + (favg - f2).

Since the average frequency is the average of the individual frequencies, we have:

favg = (f1 + f2) / 2.

Substituting this into the equation above, we get:

|f1 - f2| = (f1 + f2) / 2 - f1 + (f1 + f2) / 2 - f2,
|f1 - f2| = f1 + f2 - 2f1 + f1 + f2 - 2f2,
|f1 - f2| = 2f2 - f1 + 2f1 - 2f2,
|f1 - f2| = f2 - f1.

So, the difference between the average frequency and the frequency of one of the engines is given by:

flow - favg = f2 - favg.

And the difference between the average frequency and the frequency of the other engine is given by:

fhigh - favg = f1 - favg.

Note: The given values for the average frequency and the beat frequency are not used in these calculations. They are provided as additional information.