Sources of musical sound problem

[mikejones2000]

Question: Organ pipe A, with both ends open, has a fundamental frequency of 450 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. Use 343 m/s for the speed of sound in air.
a)How long is pipe A?

b)How long is pipe B?

I found the length of pip a by f=v/2L, or 450=343/2L, L=343/900, which is correct.

I thought I could find the length of pipe B by setting an equality like this: (5v/4L)=(2v/2(.381)). I am pretty sure I did the algebra correctly but got an incorrect answer. Any help would be greatly appreciated...

 

[J Hann]

Fundamental frequency of pipe A = 450/s
First harmonic " = 900/s
Second harmonic " = 1350/s

Fundamental length of pipe B = 1/4 wavelength
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Length of pipe B for 3d harmonic = 7/4 wavelength

Solve just as you solved for the length of pipe A

 

[kyle8921]

The sources of musical sound problem mentioned in this scenario are related to the fundamental frequency and harmonics of two organ pipes, A and B. The fundamental frequency of pipe A, with both ends open, is given as 450 Hz. This means that when air is blown through the pipe, it vibrates at a rate of 450 times per second, creating the musical sound.

The third harmonic of pipe B, with one end open, has the same frequency as the second harmonic of pipe A. This means that when air is blown through pipe B, it vibrates at a rate of 900 times per second, which is the second harmonic of pipe A. The second harmonic is the first overtone or the first multiple of the fundamental frequency.

To find the length of pipe A, we can use the formula f=v/2L, where f is the frequency, v is the speed of sound in air, and L is the length of the pipe. Substituting the given values, we get L=343/900, which is approximately 0.381 meters.

To find the length of pipe B, we need to use the formula for the second harmonic, which is f=2v/2L. Substituting the known values, we get 900=2(343)/2L, which simplifies to L=0.381 meters. This means that both pipes A and B have the same length of 0.381 meters.

The issue that you may have encountered while trying to find the length of pipe B could be due to the incorrect use of the formula. The formula for the second harmonic should be f=2v/2L, where v is the speed of sound in air and L is the length of the pipe. In your calculation, you have used a different value for v, which could have resulted in the incorrect answer.

In conclusion, the length of both pipes A and B can be found using the frequency and speed of sound in air. The fundamental frequency and harmonics play a crucial role in creating the musical sound in organ pipes. Understanding these concepts can help in solving problems related to musical sound sources.