Two strings are adjusted to vibrate at exactly 420 Hz . Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened?

423 Hz

Explanation:

The frequency of a string is given by

k is a constant representing the mode of oscillation, l is the length of the string, T is the tension and m is linear density of the string.

When other factors are constant, it is seen that as the tension increases, the frequency increases. So it is expected that the tightened string will have a higher frequency.

The beat frequency is the difference in the frequencies of both string. From the question, this beat frequency is 3 Hz. Hence, the tightened string, having a highrt frequency, has a frequency of 420 + 3 Hz = 423 Hz

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