Question

An organ pipe is 134cm long and operates at room temperature. What are the frequencies of the fundamental (n=1) and the next harmonic (n=2) if both ends of the pipe are open?

What are the frequencies of the fundamental (n=1) and the next harmonic (n=3) if one end of the pipe is closed?

Answer 1

i) When both ends are open, frequecies are given by:f=n*v/(2L), where f is frequency, n is a positive integer, v is speed of sound, L is length of the organ pipe.

Here, v= 346 m/s and L=134 cm = 1.34 m.

So, for n=1, f = 1*346/(2*1.34) = 129.1 Hz

For n=2, f=2*346/(2*1.34) = 258.2 Hz

ii)When only one end is open, frequecies are given by:f=n*v/(4L), where f is frequency, n is a positive odd integer, v is speed of sound, L is length of the organ pipe.

Here, v= 346 m/s and L=134 cm = 1.34 m.

So, for n=1, f = 1*346/(4*1.34) = 64.55 Hz

For n=3, f=3*346/(4*1.34) = 193.66 Hz