What are the first, second, and third frequencies audible from a 20 cm long organ pipe when (A) only one end is open and when (B) both ends are open. The speed of sound through the air inside the organ pipe is 343m/s

Answer 1

when one end is open, the pipe is 1/4 *nodd wavelength long.

f*lambda=v
f*4/n * .2=v
solve for f. given, n=1,3,5

both ends open, the pipe is n/2 lambda long, n =1,2,3,

f*2/n

Answer 2

(A) When only one end is open, it is a 'closed' pipe and so we use

Where fn = frequency of nth harmonic (Hz)
n = harmonic number
v = speed of sound inside the pipe (m/s)
L = length of pipe closed at one end (m)
Plugging in the values and solving, we get f1 = 428.75 Hz
f3 = 1286.25 Hz
f5 = 2143.75 Hz

(B) When both ends are open, it is an 'open' pipe and so we use

Plugging in the values and solving, we get f1 = 857.5 Hz
f2 = 1715 Hz
f3= 2572.5 Hz