Question 92: Waves

Question

An organ pipe $$40 \mathrm{~cm}$$ long is open at both ends. The speed of sound in air is $$360 \mathrm{~ms}^{-1}$$. The frequency of the second harmonic is ___________ $$\mathrm{Hz}$$.

Accepted Answer

An organ pipe that is open at both ends resonates at all harmonics, including the fundamental (first harmonic), second harmonic, third harmonic, etc.
The frequency $f$ of the $n$-th harmonic for a pipe open at both ends is given by:
$f_n = \frac{n v}{2L}$,
where:
$n$ is the number of the harmonic,
$v$ is the speed of sound, and
$L$ is the length of the pipe.
To find the frequency of the second harmonic ($n = 2$), we can substitute the given values into the formula:
$f_2 = \frac{2 	imes 360}{2 	imes 0.4} = 900 \, 	ext{Hz}$.
Therefore, the frequency of the second harmonic is $900 \, 	ext{Hz}$.

Waves

An organ pipe $40 \mathrm{~cm} long is open at both ends. The speed of sound in air is 360 \mathrm{~ms}^{-1}. The frequency of the second harmonic is ___________ \mathrm{Hz}$.

Choose the correct answer: