A section of driange culvert ` 1.23 m` in length makes a howling noise when the wind blows across its open ends .
a. Determine the frequencies of the first harmonics of the culvert , if it is cylindrical in shape and open at both ends . Take ` v = 343 m//s` as the speed of sound in air .
b. What are the three lowest natural frequencies of the culvert if it is blocked at one end ?

Explanation

The sound of the wind blowing across the end of the pipe contains many frequencies , and the culvert responds to the sound by vibrating at the natural frequencies of the air column . This example is a relatively simple substitution problem.
a. Let us first find the frequency of the first harmonic of the culvert , modelling it as an air column open at both ends .
` f_(1) = (v)/( 2L) = (343 m//s)/(2 (1.23 m)) = 139 Hz`
Find the next harmonics by multiplying by integers .
` f_(2) = 2 f_(2) = 278 Hz`
`f_(3) = 3 f_(1) = 417 Hz`
b. Find the frequency of the first harmonic of the culvert , modelling it as air column closed at one end :
`f_(1) = (v)/( 4L) = ( 343 m//s)/( 4( 1.23 m)) = 69.7 Hz`
Find the next two harmonics by multiplying by odd integers .
`f_(3) = 3 f_(1) = 209 Hz`
`f_(5) = 5 f_(1) = 349 Hz`