What is the fourth condition on wavelength for standing wave of sound in a tube of length L?

Question

What is the fourth condition on wavelength for standing wave of sound in a tube of length L?  In this case, what would be the wavelength of the sound waves if the tube is 70cm long?  If the wave speed of sound is 340 m/s, what is the frequency?  

Answer 1

Hi Megan,

 

For a standing sound wave in a tube, one end of the tube must be open ( for the sound to get in) and the other end must be closed for the sound to reflect (this is a node if one were drawing a picture).  The longest wave one could have is  λ/4 = L .  The next would be 5λ/4 = L .  i.e. one has to add a complete wave to get the next resonance (standing wave).  Then 9λ/4 = L, and 13λ/4 = L would be the fourth condition.  

 

One can now solve for  λ = 4L/13 = 0.2154 meters and use v = fy to find f = (340 m/s)/(0.2154 m) = 1540 Hz .  

 

p.s. it was 71°F here in AZ today;  how's life in NE ?