Question

a wooden tube, 1.2 meters long and open at both ends produces sound when it hits. The tube has a diameter of 3 cm. the temp in the room is 34 degrres Celcius:

a) what is the frequency if the third harmonic?

b) the tube was filled with a gas and the frequency of the fundamental was changed to 400 Hz. What is the speed of sound in the gas?

Answer 1

a)
Frequency of the n-th harmonic
   
So, for the 3rd harmonic, n = 3. And given L = 1.2 m. v = 330 m/s, we have the frequency of the 3rd harmonic is
  
If we add end corrections, then the effective length of the tube is
  
where, D is the diameter of the tube. So, we get
  
So, the frequency of the 3rd harmonic is if we add the end correction, then,
  
b)
Frequency of the fundamental is now changed to f' = 400 Hz. Then,
  
So, we get the velocity of sound in the gas is
  
If we add end correction, then,

So, we get the velocity of sound in the gas is (adding the end correction )