Question

a. A pipe closed on one end has a length L. What are the wavelengths of the first thee harmonics?

b. A pipe open on both ends has a length of 1.0 m. What are the first three resonance frequencies?

Answer 1

a)
  The closed end is a position of a node and the open end is a position of an anti-node. So,

for the first harmonic :
   
  
for the 2nd harmonic :
   
  
for the 3rd harmonic :
   
  

b)
  For the pipe with both ends open, the resonance frequencies are given by
   
where, n is an integer and v is the speed of the sound. So, putting the standard values and the given values,
   
we get
for n = 1, the frequency of the 1st harmonic
   
for n = 2, the frequency of the 2nd harmonic
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for n = 3, the frequency of the 3rd harmonic
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