Question

HELP PLEASE

A tuning fork with a period of 1.95 x 10-3 is struck at the same time as a guitar
string. If 24 beats are heard in 6.0 s, find the possible frequency or frequencies of the guitar string.

Answer 1

The possible approximate frequencies of the guitar string are 516.82 Hz and 508.82 Hz

Explanation:

The given period of the tuning fork, T₁ = 1.95 × 10⁻³ s

The number of beats in 6.0 s = 24 beats

Therefore, the beat frequency,
`f_(beat)` = 4 beats per second = 4 Hz

Let f₁ represent the frequency of the tuning fork, and let f₂ represent the frequency of the guitar string, we have;

f₁ = 1/T₁ = 1/(1.95 × 10⁻³) ≈ 512.82 Hz

We have;

`f_(beat) = \left | f_2 - f_1 \right |`

`\pm f_(beat) = f_2 - f_1`

Therefore, we get;

`4 \, Hz= \left | f_2 - 512.82 \, Hz \right |`

f₂ - 512.82 = ± 4

∴ f₂ = 512.82 ± 4

The possible frequencies of the guitar string, f₂ ≈ 516.82 Hz or f₂ ≈ 508.82 Hz