What are the three longest wavelengths for standing sound waves in a 121-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other?

Answer:A) For open pipe

1stπ=484cm

2nd wavelength=161.3cm

3rd is=96.8cm

B) For closed pipe

1st wavelength=242cm

2nd=121cm

3rd wavelength=80.7cm

Explanation:

An open pipe produces a standing waves whose wavelength is related to it's length (length of pipe) by nL/4=π, where n represent odd integers 1,2,3 ...

So the first note called fundamental note or 1st Harmonic is L=π / 4,121=π / 4

π = 121*4=484cm

Third harmonic, L=3π / 4

So π = 4l/3=4*121/3=161.3cm

The 3rd wavelength is

Fifth harmonic=

π = 4l/5=4*121/5=96.8cm

For a pipe open at one end and closed at the other also called closed pipe

Fundamental note is

2L/n = π where n=1,2,3 ... ie integers

First wavelength

π=2L=2*121=242cm

Second wavelength

π=L=121cm

Third is

π=2L/3=2*121/3=80.7cm