Question

An organ pipe open at both ends is to be designed so that the fundamental frequency it plays is 220 Hz.

a. What length of pipe is needed?

b. If one end of the pipe is stopped up, what other note (frequency) can this same pipe play?

c. Draw the fundamental frequency for the pipe open at both ends and when it is closed at one end.

d. Calculate and draw the next higher harmonic when one end of the pipe is closed.

Answer 1

a)

open both end

fn = n*v/2L where n = 1 ,2 ,3 ...

fundamental frequency when n = 1

v= speed of sound = 343 m/s

f1 = v/2L

220 = 343/ 2*L

L= 343/ ( 2*220) = 0.7795​ m

length of pipe​ = ​0.7795​ m

b)

one end of the pipe is stopped up

the frequency in this case is given by  

fn = n*v/4L where n = 1 ,3 ,5 only odd multiple

f1 = V/4L = 343/ ( 4*​0.7795​) = 110 Hz

c)

closed pipe

open both end pipe

d.

f3 = 3*v/4L = 3*f1 = 3*110 = 330 Hz

f5 = 5*f1 = 5*110 = 550 Hz

f7 = 7*f1 = 7*110 = 770 Hz and so on  

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