Calculate open pipe length given resonance.

In summary, to find the length of an open pipe needed to give resonance to a 384 Hz sound with a speed of 343 m/s, we use the equation f=\frac{nv}{2l} and solve for l by setting the frequency (384 Hz) equal to the speed of sound (343 m/s) divided by 2 times the length of the pipe (l). This gives us a length of 9.45 meters.
  • #1
seker
6
0

Homework Statement



What length of open pipe is needed to give resonance to a 384 Hz sound? Assume the speed of sound to 343 m/s.

Homework Equations



[tex]f=\frac{nv}{2l}[/tex]

The Attempt at a Solution



I am lost as to how to even start this problem.
 
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  • #2
welcome to pf!

hi seker! welcome to pf! :smile:

what is the (shortest) length (of an open pipe) needed to give a particular wavelength? :wink:
 
  • #3
This is what I have come up with so far.

[tex](384)(l)=\frac{(1)(343)}{2}[/tex]

l=9.45m
 
  • #4
looks ok! :smile:

(btw, do you understand why there's a "2" on the bottom, and would you be able to work it out for yourself in an exam if you couldn't remember the exact formula? :wink:)
 
  • #5
Can anyone provide some guidance?Sure, I'd be happy to help! First, let's review the equation given:

f = (n*v) / (2*l)

Where:
f = frequency
n = harmonic number (1, 2, 3, etc.)
v = speed of sound
l = length of the pipe

In this problem, we are given the frequency (384 Hz) and the speed of sound (343 m/s). We are asked to find the length of the pipe (l) that will give resonance at this frequency.

To solve for l, we need to rearrange the equation to isolate l on one side:

l = (n*v) / (2*f)

Now we can plug in the given values:

l = (1*343 m/s) / (2*384 Hz)

l = 0.446 m

So the length of the pipe needed to give resonance to a 384 Hz sound is approximately 0.446 meters.

Hope this helps! Let me know if you have any other questions.
 

Related to Calculate open pipe length given resonance.

1. How do you calculate the open pipe length for resonance?

The open pipe length for resonance can be calculated using the formula L = (n * λ) / 2, where L is the length of the pipe, n is the harmonic number, and λ is the wavelength of the sound wave.

2. What is the significance of calculating open pipe length for resonance?

Calculating the open pipe length for resonance allows us to determine the natural frequency of the pipe, which is the frequency at which it will vibrate most efficiently. This is important in understanding the behavior of sound waves and the production of musical tones.

3. What factors affect the open pipe length for resonance?

The open pipe length for resonance is affected by the speed of sound, the density of the medium, and the harmonic number. It is also influenced by the shape and material of the pipe.

4. Can the open pipe length for resonance be calculated for any type of pipe?

Yes, the open pipe length for resonance can be calculated for any type of pipe, as long as it is open at both ends and can support standing waves. This includes pipes made of various materials such as metal, wood, or plastic.

5. How is the open pipe length for resonance used in real-world applications?

The calculation of open pipe length for resonance is used in various fields, including music, engineering, and physics. In music, it helps in understanding the production of musical tones and the design of musical instruments. In engineering, it is used in the design of acoustic systems, such as speakers and wind instruments. In physics, it is used to study the behavior of sound waves and their interactions with different media.

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