Chapter 12, Problem 36P

To determine

The length the pipe.

To identify: Whether it is open or closed.

Answer to Problem 36P

L = 4.28 m and it is a open pipe.

Explanation of Solution

Given:

Resonates at frequencies = 240 Hz, 280 Hz

Formula used:

  $L=\frac{v}{2f}\text{ m}\text{.}$

Calculation:

The difference of two harmonics is given as 280 Hz - 240 Hz = 40 Hz.

If is closed at one end then the fundamental frequency should have to be 20 Hz.  Since there are no even harmonics, so the difference must be for two harmonics only.  This will give two harmonics (12th and 14^th) that are not possible. Therefore, the tube is open on both ends.

  $f=\frac{v}{2L}\text{ Hz}\text{.}$

  $L=\frac{v}{2f}\text{ m}\text{.}$

  $v=331(0.6\times 20)\text{ m/s}$

  $v=343\text{ m/s}$

The velocity of sound wave is 343 m/s.

Now substitute the values in the equation L

  $L=\frac{v}{2f}\text{ Hz}\text{.}$

  $\begin{array}{l}L=\frac{343}{2\times 40}\text{ m}\text{.}\\ L=4.28\text{ m}\end{array}$

Conclusion:

The length of the pipe is 4.28 m and it is the open pipe which has all harmonics.