Question

An organ pipe is open at both ends has a length of 3 m. What is the second longest harmonic wavelength for sounds waves in this pipe?

Answer 1

Harmonic sound waves are produced inside the pipe whenever a multiple of half the wavelength of the sound waves matches the length of the pipe:

`n((\lambda)/(2))=L`

Where L is the length of the pipe, n is an integer and λ is the wavelength of the sound waves.

The smaller the integer n is, the greater the wavelength will be. Then, to find the second longest harmonic wavelength, set n=2:

`\begin{gathered} \Rightarrow2((\lambda)/(2))=L \\ \Rightarrow\lambda=L \end{gathered}`

Substitute L=3m to find the second longest wavelength for sound waves in the pipe:

`\lambda=3m`

Therefore, the second longest harmonic wavelength for sound waves in that pipe is:

`3m`