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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.

Answer and Explanation:

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.


Learn more about this topic:

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Interference Patterns of Sound Waves

from MTEL Physics (11): Practice & Study Guide

Chapter 16 / Lesson 5
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