Question

A piano tuner hears a beat every 2.20 s when listening to a 266.0 Hz tuning fork and a single piano string. What are the two possible frequencies (in Hz) of the string? (Give your answers to at least one decimal place.)

Answer 1

The lower frequency is
`f_1 = 265.55 \ Hz`

The higher frequency is
`f_2 = 266.4546 \ Hz`

Step-by-step explanation:

From the question we are told that

The period is
`T = 2.20 \ s`

The frequency of the tuning fork is
`f = 266.0 \ Hz`

Generally the beat frequency is mathematically represented as

`f_b = (1)/(T)`

substituting values

`f_b = (1)/(2.20)`

`f_b = 0.4546 \ Hz`

Since the beat frequency is gotten from the beat produced by the tuning fork and and the string then

The possible frequency of the string ranges from

`f_1 = f- f _b`

to

`f_2 = f + f_b`

Now substituting values

`f_1 = 266.0 - 0.4546`

`f_1 = 265.55 \ Hz`

For
`f_2`

`f_2 = 266 + 0.4546`

`f_2 = 266.4546 \ Hz`