Relating resonance with two different Pipes

In summary, the question asks for the length of pipe A that will result in the third lowest resonant frequency of pipe A being equal to the lowest resonant frequency of pipe B. The formula for calculating frequency is given, as well as the specific harmonics that need to be considered. The student is unsure of how to set up the problem and is looking for a hint to guide them.
  • #1
RoxSox2004
2
0

Homework Statement



A pipe, open at one end, has a leng
produces pipe A, open at one end, and pipe B, o

A pipe, open at one end, has a length L. Cutting this pipe crosswise
produces pipe A, open at one end, and pipe B, open at both ends.
a. For what length of pipe A will the third lowest resonant frequency of pipe A be equal
to the lowest resonant frequency of pipe B?


Homework Equations



v = (lambda)(f)

5th harmonic of A, f = (5v)/(4L)
1st Harmonic of B, f = v/2L

The Attempt at a Solution



I've been fairly stumped by this one. I don't get exactly how to set it up. I tried setting the frequencies equal to each other, but it doesn't work.
 
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  • #2
I'm really just looking for a hint to set me on the right path.
 

Related to Relating resonance with two different Pipes

1. How does resonance occur in two different pipes?

Resonance occurs in two different pipes when they are set in motion by a vibrating source, such as a sound wave or mechanical force, causing them to vibrate at the same natural frequency. This results in an amplification of the sound produced by the pipes.

2. What factors affect the resonance of two different pipes?

The length, diameter, and material of the pipes, as well as the surrounding medium, all play a role in the resonance of two different pipes. The properties of the vibrating source and the distance between the two pipes also impact the resonance.

3. How can resonance be demonstrated in two different pipes?

One way to demonstrate resonance in two different pipes is by using a tuning fork to create a sound wave and holding it near the opening of one of the pipes. The pipe will start to vibrate and if the other pipe is tuned to the same frequency, it will also start to vibrate, producing a louder sound.

4. What practical applications does resonance in two different pipes have?

Resonance in two different pipes has practical applications in musical instruments, such as wind instruments, where the length and diameter of the pipes can be adjusted to produce different notes. It is also used in engineering to design structures that can withstand vibrations, such as bridges and buildings.

5. Can resonance in two different pipes be harmful?

In some cases, resonance in two different pipes can be harmful, such as in the case of a vibrating pipe in a building or bridge, which can lead to structural damage. It can also be harmful to the human body if exposed to loud and prolonged sounds at the resonant frequency. Proper precautions should be taken to avoid these potential dangers.

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