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

• confused1
In summary, the beat frequency problem is a phenomenon that occurs when two waves of different frequencies interfere with each other, resulting in a perceived fluctuation in sound. This occurs due to a difference in frequencies, amplitudes, and phase differences. The beat frequency can be calculated by taking the difference between the two frequencies and dividing it by the number of beats per second. Real-life applications of this problem include audio engineering, tuning musical instruments, and studying brain activity.
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 = ?

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.

## 1. What is the beat frequency problem?

The beat frequency problem is a phenomenon that occurs when two waves of different frequencies are played simultaneously. It results in a perceived fluctuation in the overall sound, known as a "beat".

## 2. How does the beat frequency problem occur?

The beat frequency problem occurs when two waves of similar amplitude but slightly different frequencies interfere with each other. This causes the waves to periodically reinforce and cancel each other out, resulting in the perceived beat.

## 3. What factors affect the beat frequency?

The beat frequency is affected by the difference in frequencies between the two waves, as well as their amplitudes and phase differences. The closer the frequencies are, the slower the beat, and the larger the difference, the faster the beat.

## 4. How is the beat frequency calculated?

The beat frequency can be calculated by taking the difference between the two frequencies and dividing it by the number of beats per second. This can also be represented mathematically as fbeat = |f1 - f2|.

## 5. What are some real-life applications of the beat frequency problem?

The beat frequency problem has various applications in science and technology, including audio engineering, tuning musical instruments, and studying brain activity. It is also used in experiments to measure the speed of sound and in radio communication to tune frequencies.

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