Question

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 1

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