An organ pipe open at both ends has two successive harmonics with frequencies of and .What is the length of the pipe? The speed of sound is in air.
A) 5.25 m
B) 5.73 m
C) 2.76 m
D) 4.90 m
E) 3.62 m

Question

An organ pipe open at both ends has two successive harmonics with frequencies of  and  .What is the length of the pipe? The speed of sound is  in air.
A) 5.25 m 
B) 5.73 m 
C) 2.76 m 
D) 4.90 m 
E) 3.62 m

Quizplus · Accepted Answer

The fundamental frequency of an open organ pipe is given by:

f1 = v/2L

Where v is the speed of sound and L is the length of the pipe.

The two successive harmonics are given by:

f2 = 2f1 = v/L and f3 = 3f1 = 3v/2L

We can solve for L by setting f2 and f3 equal to the given frequencies and solving for L:

v/L = 11ea83ea_6a0e_ebbb_aeff_9f842bfec076_TB6394_11

3v/2L = 11ea83ea_6a0e_ebba_aeff_157e9239a33d_TB6394_11

Dividing the second equation by the first and simplifying, we get:

1.5 = 11ea83ea_6a0e_ebba_aeff_157e9239a33d_TB6394_11 /11ea83ea_6a0e_ebbb_aeff_9f842bfec076_TB6394_11

1.5 = 10.83333

L = v/(1.5*f2) = 5.73 m

Therefore, the answer is B) 5.73 m.

An Organ Pipe Open at Both Ends Has Two Successive