Atuner first tunes the a string very precisely by matching it to a 440 hz tuning fork. she then strikes the a and e strings simultaneously and listens for beats between the harmonics. what beat frequency between higher harmonics indicates that the e string is properly tuned

The beat frequency is 2 Hz.

Explanation:

Given that,

Frequency of A = 440 Hz

Frequency of E = 659 Hz

Suppose, piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have a frequency of 440 Hz and the note E should be at 659 Hz.

We need to calculate the third harmonic of A

Using formula of harmonic

Put the value into the formula

We need to calculate the second harmonic of E

Using formula of harmonic

Put the value into the formula

We need to calculate the beat frequency

Using formula of beat frequency

Put the value into the formula

Hence, The beat frequency is 2 Hz.

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