The lowest tone to resonate in pipe of length L that is open at both ends is 200 Hz.Which one of the following frequencies will not resonate in the same pipe?
A)200 Hz
B)400 Hz
C)600 Hz
D)800 Hz
E)900 Hz

Question

Quizplus · Accepted Answer

For a pipe open at both ends, the resonant frequencies are given by:
$f_n = \frac{n}{2L}v$, where n is an integer and v is the speed of sound.
The lowest frequency is when n=1, so we have 
$200 Hz = \frac{1}{2L}v$
Thus, $L = \frac{v}{2(200 Hz)}$
For the other frequencies to resonate in the same pipe, they must satisfy the same equation with different values of n. Plugging in the values given, we get:
B) $400 Hz = \frac{2}{2L}v$, which satisfies the equation
C) $600 Hz = \frac{3}{2L}v$, which satisfies the equation
D) $800 Hz = \frac{4}{2L}v$, which satisfies the equation
E) $900 Hz = \frac{9}{2L}v$, which does not satisfy the equation.
Therefore, only E will not resonate in the same pipe.

The Lowest Tone to Resonate in Pipe of Length L