Question

When a piano tuner strikes both the A on the piano and a 440 Hz tuning fork, he hears a beat every 2 seconds. The frequency of the piano's A is

Answer 1

The frequency is
`f = 439.5 \ Hz`

Step-by-step explanation:

From the question we are told that

The frequency of the tuning fork is
`f_t = 440 \ Hz`

The beat period is
`T = 2 \ s`

Generally the beat frequency is mathematically represented as

`f_b = (1)/(T)`

`f_b = (1)/(2)`

`f_b = 0.5 \ Hz`

The beat frequency is also represented mathematically as

`f_b = f_t - f`

Where
`f` is the frequency of the piano

So

`f = 440 - 0.5`

`f = 439.5 \ Hz`