## A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second.

Question

A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second. Next, a bit of tape is put onto each tine of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin string. What is the frequency of the string?

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6 months 2021-07-20T21:05:28+00:00 2 Answers 17 views 0

The frequency of the string is 266 Hz

Explanation:

The frequency of the instrument is equal:

Where

fbeat = beat frequency = 4 Hz

ffork = frequency of the fork = 262 Hz

Replacing:

Explanation:

Firstly, it should be noted that the beats being heard are the beat frequencies

And the formula for that is

Beat frequency = Frequency of instrument – Frequency of the fork

Also, the less the beats are, the closer an instrument can be close to being in tune

For example, if you tape the ends of the fork, you are more or less, dampening the frequency of the fork

Now, we know that the frequency of the mandolin is either 258 or 266 Hz. However when you drop the pitch, you get another beat frequency (aka farther out of tune)

Thus, it can only be the higher number which is 266 Hz

Therefore, the frequency of the strings is 266 Hz