Organ pipe A is closed on one end Organ pipe B is open on both ends. Frequency o

Question

Organ pipe A is closed on one end Organ pipe B is open on both ends. Frequency of 5th harmonic (f5(A) =5f1(A) of pipe A is the same as the frequency of the 2ndharmonic (f2(B) = 2f1(B) of pipe B. Length of pipe A is LA= 5.40 m. Assume speed ofsound in air is V=344 m/s Neglect all end-correction effects for pipe A x=0 at left end of pipe and x=LA atright end of pipe For pipe B x=0 at left end of pipe and x = LB atright end of pipe Calculate position of first pressure node away from open endof pipe A (x=LA) when its 5th harmonic is excited What is wavelength of B of second harmonic ofpipe B What is frequency of the 1st harmonic (fundamental ) of pipeB Organ pipe A is closed on one end Organ pipe B is open on both ends. Frequency of 5th harmonic (f5(A) =5f1(A) of pipe A is the same as the frequency of the 2ndharmonic (f2(B) = 2f1(B) of pipe B. Length of pipe A is LA= 5.40 m. Assume speed ofsound in air is V=344 m/s Neglect all end-correction effects for pipe A x=0 at left end of pipe and x=LA atright end of pipe For pipe B x=0 at left end of pipe and x = LB atright end of pipe Calculate position of first pressure node away from open endof pipe A (x=LA) when its 5th harmonic is excited What is wavelength of B of second harmonic ofpipe B What is frequency of the 1st harmonic (fundamental ) of pipeB

Explanation / Answer

Organ pipe A is closed on one end, so LA =1(A)/2 , f1(A) =v/1(A) = v/(2LA) Organ pipe B is open on both ends so LB =1(B)/4, f1(B) = v/1(B)= v/(4LB) Frequency of 5th harmonic (f5(A) =5f1(A) of pipe A is the same as the frequency of the 2ndharmonic (f2(B) = 2f1(B) of pipe B.
so 5v/(2LA) = 2v/(4LB)
LB = LA/5
Length of pipe A is LA= 5.40 m.
so LB = 1.08 m

V=344 m/s
Calculate position of first pressure node away from open endof pipe A (x=LA) when its 5th harmonic is excited
LA = 5A/4, the position isA/4 = 1.08 m away from open end of pipe

What is wavelength of B of second harmonic ofpipe B
LB = 32(B)/4, so 2(B)= 1.44 m

What is frequency of the 1st harmonic (fundamental ) of pipeB
f1(B) = v/(4LB) = 79.6 Hz

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