Chapter 26, Problem 52A

Two notes are sounding, one of which is 440 Hz. If a beat frequency of 5 Hz is heard, what is the other note’s frequency?

To determine

To Calculate: The frequency of other note on the basis of given information.

Answer to Problem 52A

The frequency of other can be $435Hz$ or $445Hz$ .

Explanation of Solution

Given info:

Frequency of one note, ${\mathrm{f}}_1=440Hz$

Beat frequency, ${\mathrm{f}}_{beat}=5Hz$

Formula used:

  ${\mathrm{f}}_{beat}=\left|f_2-f_1\right|$

Calculation:

Substituting the given values,

  $\begin{array}{l}{f}_{beat}=\left|f_2-440\right|\\ 5=\left|f_2-440\right|\\ or,\\ f_2-440=\pm 5\\ f_2=440+5,f_2=440-5\\ f_2=445Hz,435\mathrm{Hz}\end{array}$

Conclusion:

The frequency of other can be $435Hz$ or $445Hz$ .