What Causes the Pulsating Sound from a Jet's Engines?

[confused1]

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 two seconds. The average frequency you hear is 4100 Hz. What is the difference between the individual frequencies of the sounds from each engine and this average?

f_low-f_ave = ?

f_high-f_ave = ?

 

[OlderDan]

Find out what you can about "beat frequency", and see what you can do with it.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html

 

[thepatientmental]

The difference between the individual frequencies of the sounds from each engine and the average frequency is 4100 Hz. This phenomenon is known as the beat frequency problem, where two sound waves with slightly different frequencies interfere with each other, resulting in a pulsating sound.

To calculate the individual frequencies, we can use the formula f = (c/2L) * n, where c is the speed of sound, L is the distance between the engines, and n is the number of nodes produced by the interference pattern. Since we know the average frequency (f_ave) and the time interval (T) between the beats (2 seconds), we can calculate the speed of sound (c) using the formula c = f_ave * T.

Substituting the values, we get c = 4100 Hz * 2 seconds = 8200 m/s.

Assuming that the distance between the engines is 2 meters, we can calculate the individual frequencies as follows:

f_low = (8200/2*2) * 1 = 2050 Hz

f_high = (8200/2*2) * 3 = 6150 Hz

Therefore, the difference between the individual frequencies and the average frequency is:

f_low - f_ave = 2050 Hz - 4100 Hz = -2050 Hz

f_high - f_ave = 6150 Hz - 4100 Hz = 2050 Hz

In conclusion, the difference between the individual frequencies and the average frequency is 2050 Hz. This is because the lower frequency engine produces a sound wave that is 2050 Hz lower than the average frequency, while the higher frequency engine produces a sound wave that is 2050 Hz higher than the average frequency. This difference in frequencies results in the beat frequency that we hear.