Chapter 15, Problem 8STP

To determine

To Calculate: The speed of the sound.

Answer to Problem 8STP

  $\text{328 m/s}$

Explanation of Solution

Given:

First resonance length of the closed air column, $L=16.8\text{cm}$

Frequency of the sound, $f=488\text{Hz}$

Formula Used:

For closed pipe, the relation between first resonance length $\left(L\right)$ , frequency $\left(f\right)$ and speed of sound $\left(v\right)$ is:

  $f=\frac{v}{4L}$

Calculations:

Re-arrange the formula, substitute the values and solve.

  $\begin{array}{l}f=\frac{v}{4L}\\ v=f\times 4L\\ v=488\text{Hz}\times 4\times 0.168\text{m}\\ \text{v}\approx \text{328 m/s}\end{array}$

Conclusion:

Thus, the speed of the sound is $\text{328 m/s}$ .