A music tuner uses a 554-Hz tuning fork to tune the frequency of a musical instrument. If the...

Question:

A music tuner uses a 554-Hz tuning fork to tune the frequency of a musical instrument. If the tuner hears a beat frequency of 2 Hz, what is the frequency of the instrument?

A. It must be 556 Hz

B. It must be 552 Hz

C. It could be either 556 Hz or 552 Hz

D. It could be either 553 Hz or 555 Hz

E. It is neither 556 Hz or 552 Hz

Tuning Fork:

The tuning fork is a metallic U shaped device having fork that is used to create resonance. The resonance created by the tuning fork is of the constant pitch, thus creating the original musical tone. It is invented by the British musician in the year 1711.

Answer and Explanation:


Given data

  • The frequency of the tuning fork is: {eq}f = 554\,{\rm{Hz}}{/eq}
  • The beat frequency of the tuner hears is: {eq}\Delta f = 2\,{\rm{Hz}}{/eq}


Let {eq}f'{/eq} be the frequency of the instrument,

Then the expression for calculating the frequency,

{eq}\begin{align*} \Delta f &= f \sim f'\\ f'& = f \pm \Delta f \end{align*}{/eq}


Substituting the value in the above expression,

{eq}\begin{align*} f'& = 554 + 2\\ f' &= 556\,{\rm{Hz}}\\ f' &= 554 - 2\\ f' &= 552{\rm{Hz}} \end{align*}{/eq}


Thus, the option (c) is correct which is it could either be 556 Hz or 552 Hz.


Learn more about this topic:

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How to Find the Frequency of a Trig Function

from High School Precalculus: Help and Review

Chapter 21 / Lesson 11
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