Organ pipe A, with both ends open, has a fundamental frequency of 225 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are

To find the length of the organ pipes, we can use the formula for the fundamental frequency of an open-open organ pipe:

f = (v/2L) * n

Where:
f is the frequency of the pipe's harmonic
v is the speed of sound in air (approximately 343 m/s at room temperature)
L is the length of the pipe
n is the harmonic number

For organ pipe A:
f1 = 225 Hz (fundamental frequency)
n1 = 1 (fundamental frequency is the first harmonic)

For organ pipe B:
f2 = 2f1 = 2 * 225 = 450 Hz (second harmonic)
n2 = 3 (third harmonic)

Since both pipes have the same frequency for these specific harmonics, we can set up the equations:

(343/2LA) * 1 = (343/2LB) * 2
(343/2LA) = (343/2LB) * 2

Simplifying the equation:

LA = 2 * LB

It means that the length of organ pipe A is twice the length of organ pipe B.

Since we don't have a specific value for one of the lengths, we won't be able to find the exact lengths of the pipes. However, we can determine their ratios.

Let's assume the length of organ pipe B is L. According to the equation above, the length of organ pipe A would be 2L.

Therefore, the length ratio is:
LA : LB = 2L : L = 2 : 1

In conclusion, the length of organ pipe A is twice the length of organ pipe B, but specific values for the lengths cannot be determined without additional information.