Chapter 12, Problem 89GP

To determine

The fundamental frequency for the standing wave in the room.

Answer to Problem 89GP

  $34\text{Hz},43\text{Hz}\&61\text{Hz}$

Explanation of Solution

Given:

The length of the room, $\mathrm{L}=5\text{m}$

The breadth of the room, $\mathrm{B}=4\text{m}$

The height of the room, $\mathrm{H}=2.8\text{m}$

Formula used:

The fundamental frequency is calculated as:

  $\mathrm{f}=\frac{\mathrm{V}}{2\mathrm{L}}$

Here, V is the speed of sound and L is the length

Calculation:

Calculate the fundamental frequency for the given length of room.

  ${\mathrm{f}}_{\mathrm{L}}=\frac{343}{2(5)}=34.3\text{Hz}=34\text{Hz}$

Calculate the fundamental frequency for the given breadth of room.

  ${\mathrm{f}}_{\mathrm{B}}=\frac{343}{2(4)}=42.9\text{Hz}=43\text{Hz}$

Calculate the fundamental frequency for the given height of room.

  ${\mathrm{f}}_{\mathrm{H}}=\frac{343}{2(2.8)}=61.25\text{Hz}=61\text{Hz}$

Conclusion:

The fundamental frequency for $\text{5}\text{m}$ length is $34\text{Hz}$ , $43\text{Hz}$ for the $4\text{m}$ breadth, and $61\text{Hz}$ for the $\text{2}.\text{8 m}$ height.