Chapter 12, Problem 83GP

To determine

The length of longer organ pipe.

Answer to Problem 83GP

  $\text{2}\text{.84}\text{m}$

Explanation of Solution

Given:

The beat frequency, $\mathrm{\Delta }\mathrm{f}=11\text{Hz}$

Length of the shorter string, ${\mathrm{L}}_1=2.4\text{m}$

Formula used:

The fundamental frequency ${\mathrm{f}}_1$ of organ pipe is given as:

  $\begin{array}{l}{\mathrm{f}}_1=\frac{\mathrm{V}}{2{\mathrm{L}}_1}\\ \mathrm{V}=343\text{m/s}\\ {\mathrm{L}}_1=2.4\text{m}\end{array}$

  $\begin{array}{l}\mathrm{\Delta }\mathrm{f}={\mathrm{f}}_1-{\mathrm{f}}_2\\ {\mathrm{L}}_2=\frac{\mathrm{V}}{2{\mathrm{f}}_2}\end{array}$

Calculation:

Substitute the given values:

  $\begin{array}{l}{\mathrm{f}}_1=\frac{343}{2(2.4)}=71.46\text{Hz}\\ {\mathrm{f}}_2=71.46-11=60.46\text{Hz}\\ {\mathrm{L}}_2=\frac{343}{2(60.46)}\\ {\mathrm{L}}_2=2.84\text{m}\end{array}$

Conclusion:

The length of longer pipe is $2.84\text{m}$ .