how do i solve this problem?

Question

The range of human hearing is roughly from twenty hertz to twenty kilohertz. Based on these limits and a value of 340 m/s for the speed of sound, what are the lengths of the longest and shortest pipes (open at both ends and producing sound at their fundamental frequencies) that you expect to find in a pipe organ?
....................................... m (shortest pipe)
......................................m (longest pipe)

Answer 1

u dont think i wud ur homework when i dont do mine...do ya?

Answer 2

Twenty Hertz means that the vibration has twenty cycles per second. With a speed of sound of 340 m/s, this means the wavelength of the 20 Hz sound is 17 m long. That would be the leght of a pipe organ tube able to produce that low frequency as a fundamental tone.
At the other end of the spectrum, a tone of 20 kHz would have a wavelenght 1000 times shorter at 0.017 m ( 17 mm or 1.7 cm ).

Answer 3

Resonant frequency of a pipe open at both ends is given by:

f = nv/2L, where n is an integer (1, 2, 3, ... ), v is the velocity of sound, and L is the length of the pipe.

Solving for L:

L = nv/2f

and substituting 340 m/s for v, 20 hertz for f, and n = 1 (for the fundamental or lowest resonant frequency):

L = 340 / 40 = 8.5 meters at 20 Hz (longest pipe)
L = 340 / 40000 = 0.085 meters at 20 kHz (shortest pipe)

Answer 4

You're going to need the formula for the frequency produced by a pipe open at both ends. I presume you've already been told this in your course, so go and look it up.

Answer 5

Duuuuuuuuuuuuuuuuh