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If a piano tuner hears 3 beats each second when listening to a 8 Hz tuning fork and a single...

Question:

If a piano tuner hears 3 beats each second when listening to a 8 Hz tuning fork and a single string on the piano which is of higher frequency.. What is the frequency of the single string from the piano?

Beat frequency

Beats occur when two sound waves of slightly different frequencies {eq}f_a {/eq} and {eq}f_b < f_a {/eq} interferes. The beat frequency, or the number of beats per unit of time, is

{eq}f_\text{beat} = f_a - f_b. {/eq}.

Answer and Explanation:

Since the string on the piano is the one with higher frequency, let it be denoted by {eq}f_a {/eq}. Given that {eq}f_b = 8 \ \text{Hz} {/eq} and {eq}f_\text{beat} = 3 \ \text{Hz} {/eq} (3 beats per second), then

{eq}f_\text{beat} = f_a - f_b \quad \Rightarrow \quad f_a = f_\text{beat}+f_b = 3 \ \text{Hz} + 8 \ \text{Hz} = 11 \ \text{Hz}. {/eq}

Therefore, the frequency of the piano string is 11 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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