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. (Hint: if a harmonic does not exist, it would not be heard.)

A) The answers are:

the first frequency - 428.75 Hz

the second frequency - 1286.25 Hz

the third frequency - 2143.75 Hz

The frequency (when the pipe is closed) is: f = v (2n - 1) / 4L

v - the speed of sound

n - the frequency order

L - the length of the organ pipe

We know:

v = 343 m/s

L = 20 cm = 0.2 m

1. The first frequency (n = 1):

f = 343 * (2 * 1 - 1) / 4 * 0.2 = 343 * 1 / 0.8 = 428.75 Hz

2. The second frequency (n = 2):

f = 343 * (2 * 2 - 1) / 4 * 0.2 = 343 * 3 / 0.8 = 1286.25 Hz

3. The third frequency (n = 3):

f = 343 * (2 * 3 - 1) / 4 * 0.2 = 343 * 5 / 0.8 = 2143.75 Hz

B) The answers are:

the first frequency - 857.5 Hz

the second frequency - 1715 Hz

the third frequency - 2572.5 Hz

The frequency (when the pipe is open) is: f = vn/2L

v - the speed of sound

n - the frequency order

L - the length of the organ pipe

We know:

v = 343 m/s

L = 20 cm = 0.2 m

1. The first frequency (n = 1):

f = 343 * 1 / 2 * 0.2 = 343 / 0.4 = 857.5 Hz

2. The second frequency (n = 2):

f = 343 * 2 / 2 * 0.2 = 686 / 0.4 = 1715 Hz

3. The third frequency (n = 3):

f = 343 * 3 / 2 * 0.2 = 1029 / 0.4 = 2572.5 Hz