Inside a spinet, the hammer is sometimes set to strike multiple strings to increase the instruments volume. Of the 523 Hz note has two strings, and one slips from its normal tension of 620 N to 610 N, what beat frequency in Hz is heard when the note is played?

4 Hz

Explanation:

The frequency of a string is given by

where k is a constant that determines the mode of the vibration,

l is the length of the string,

T is the tension in the string,

is the linear density or mass per unit length of the string

It follows that f is directly proportional to provided other factors are constant.

This relation is expressed as

is the frequency when tension is and is the frequency when tension is .

The beat frequency is the difference in the frequencies. Hence,

f = 523 - 519 = 4 Hz

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