Length of the closed end pipe,
l = 20 cm = 0.2 m
Speed of sound, v = 340 ms-1
The fundamental frequency, v = v/4l = {340}/{4 x 0.2}
= 425 Hz
This is the first harmonic. The second harmonic is 3v i.e., 1275 Hz, the third harmonic is 5v i.e., 2125 Hz etc. Therefore only the first harmonic of frequency 425 Hz is resonantly excited by a 430 Hz source.
If both the ends of the pipe are open, the fundamental frequency is given by:
v' = v/2l = {340}/{2 x 0.2} = 850 Hz
The second, third, fourth ... etc. harmonics have frequencies 2v', 3v', 4v', ....i.e., 1700 Hz, 2550 Hz, 3400 Hz. etc. No harmonic can be excited by the 430 Hz source in this case.
