Asection of driange culvert1.23 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 . Takev = 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 ?

Asection of driange culvert1.23 m in length makes a howling noise when

1.	Asection of driange culvert1.23 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 . Takev = 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 ?
Answer» SOLUTION :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`