String instrument players can tune one string off of another - once you are happy with the tension and resulting pitch in one lower string, you put your finger down partway up the first string at the appropriate spot to make a higher pitch, one which should match the fundamental pitch of the next string over. If the second string is almost, but not quite properly tuned, you will hear beats. Suppose you are doing this, and hear one beat every 0.88 s when trying to adjust the second string. If the first string (with your finger on it) is playing at 114 Hz how far off in frequency is the second string?

Question

String instrument players can tune one string off of another - once you are happy with the tension and resulting pitch in one lower string, you put your finger down partway up the first string at the appropriate spot to make a higher pitch, one which should match the fundamental pitch of the next string over. If the second string is almost, but not quite properly tuned, you will hear beats. Suppose you are doing this, and hear one beat every 0.88 s when trying to adjust the second string. If the first string (with your finger on it) is playing at 114 Hz how far off in frequency is the second string?

I figured 100Hz incorrect

Answer 1

The beat frequency is 1/0.88 = 1.14 Hz.

That equals the difference in frequencies

Answer 2

To calculate the frequency difference between the first and second strings, we need to use the information about the number of beats and the time interval between them.

The number of beats per second is equal to the difference in frequencies between the two strings. In this case, we are hearing one beat every 0.88 seconds.

To find the frequency difference:

Frequency difference = 1 / Time interval of beats

Frequency difference = 1 / 0.88 s

Frequency difference ≈ 1.136 Hz

Therefore, the second string is off in frequency by approximately 1.136 Hz from the first string.