# A guitarist is tuning a guitar. She hears a low beat every 4.0 seconds. What is the difference...

## Question:

A guitarist is tuning a guitar. She hears a low beat every 4.0 seconds. What is the difference between the correct frequency and measured frequency of the guitar string?

## The Beat Frequency

If two wave sources with slightly differing frequencies {eq}\displaystyle {\nu_1} {/eq} and {eq}\displaystyle {\nu_2} {/eq} generate waves at the same time and these waves superpose then an interference effect in time will occur. The intensity is found to oscillate in time with a frequency {eq}\displaystyle {\nu} {/eq} called the beat frequency. It is given by,

{eq}\displaystyle {\nu = \pm (\nu_1-\nu_2)}-----------(1) {/eq}.

This can be utilized for tuning musical instruments with the help of a known reference frequency. By sounding the two frequencies together and adjusting the instrument till the beats disappear the correct frequency is attained.

The guitarist hears one beat every 4 seconds. Therefore the beat frequency is {eq}\displaystyle {\frac{1}{4}\ Hz} {/eq}.

Since the beat frequency is the difference between the two different frequencies which are sounded together it follows that the correct frequency and the measured frequency differ by 0.25 Hz.