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A piano tuner hears one beat every 4.0 s when trying to adjust two strings, one of which is sounding 370 Hz.

a. Identify the frequency of the other string
b. Explain the concept of beats in sound
c. Discuss the relationship between beat frequency and tuning
d. Calculate the beat frequency in hertz

1 Answer

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Final answer:

The other string can have frequencies of either 262.0 Hz or 266.0 Hz. Beats in sound occur when two sound waves with slightly different frequencies interfere with each other. The beat frequency is the difference in frequency between the two waves, and it can be calculated by subtracting one frequency from the other.

Step-by-step explanation:

a. The frequency of the other string can be found by subtracting the beat frequency from the frequency of the tuning fork. In this case, the beat frequency is 2.00 Hz, and the frequency of the tuning fork is 264.0 Hz. So, the frequency of the other string can be either 262.0 Hz or 266.0 Hz.

b. Beats in sound occur when two sound waves with slightly different frequencies interfere with each other. This interference produces a periodic variation in the loudness of the sound, which is perceived as a beating or pulsating sound.

c. The relationship between beat frequency and tuning is that when two sound waves with very similar frequencies interfere, the resulting beat frequency is equal to the difference in frequency between the two waves. Tuning is done by adjusting the frequency of one of the waves until the beat frequency becomes zero, indicating that the frequencies of the two waves are the same.

d. The beat frequency can be calculated by subtracting the frequency of one wave from the frequency of the other wave. In this case, the beat frequency would be 2.00 Hz.

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