Frequency of sound in a pipe question

In summary, when the pipe is lowered, standing waves will be created. The frequency of the sound will be equal to (4n+1)c/4L.
  • #1
magiclink
23
0

Homework Statement


Shown in the picture attachment.

The Attempt at a Solution


Hello! with this question I am just completely lost. I haven't the slightest clue how to get started. Anybody care to explain why the answer is D? (I've looked at the markscheme..)
 

Attachments

  • Frequency question.jpg
    Frequency question.jpg
    11.3 KB · Views: 426
Physics news on Phys.org
  • #2
magiclink said:

Homework Statement


Shown in the picture attachment.

The Attempt at a Solution


Hello! with this question I am just completely lost. I haven't the slightest clue how to get started.

their will be loud sound when stationary waves will be formed...(it's key point for this question)
for such cases(when one end closed and one end open)
f=(4n+1)c/(4L)
for both the cases f is constant c(speed of sound) is constant.
in first cases take n=k and in second case take it k+1. you will have two equations having a single variable k. just eliminate it and you will get speed of sound in terms of L1 L2 and f.
magiclink said:
Anybody care to explain why the answer is D? (I've looked at the markscheme..)
it's bad habit. looking at answer and trying to somehow explain that...
I have not done it. but i think my solution will work.
 
Last edited:
  • #3
Hi! being quite a simpleton, I found the answer a bit confusing. I understand that as the pipe is lowered standing waves will be produced... I also get that f is constant as the tuning fork held determines what possible lengths that cause the louder sounds. Why will the frequency be equal to (4n+1)c/4L then though? I'd figure that the wavelength at L1 of the sound in the pipe would be 4L, but then how does that translate into the equation you presented? Sorry i'f I'm a little inept! Thankyou for your help thus far.
 
  • #4
NOTE: i have done an error in my last post formula is not f=(4n+1)c/(4L) it is f=(2n+1)c/(4L)..
magiclink said:
Why will the frequency be equal to (4n+1)c/4L then though?

You might have seen it's derivation in your book...
there will be a node at closed end and anti node and open end..
I'd figure that the wavelength at L1 of the sound in the pipe would be 4L
that is not necessary...
what if is say it is 4L/3. or 4L/5..
that can be any out of this series..

λ/4=L(fundamental wave)
3λ/4=L (first overtone)
5λ/4=L(second overtone)
..
..
..
(2n+1)λ/4=L (replace λ by c/f to get frequency formula as i have written in my last post)

but as it is stated in question that large sound listened first time when distance is L1 and very next is L2 so if in case of L1 n=k then in case of L2 it is (k+1)..
if you are still not clear that what's happening then once again read this topic from your book ...
 
Last edited:
  • #5
Resonance occurs for pipe lengths such that there is a displacement node at the closed end and a displacement antinode at,approximately,the open end.First resonance occurs for a length of L1 when 1/4 of the wave fits in the space.Second resonance occurs for a length of L2 when 3/4 of a wave fits in the space.From that you can work out the wavelength in terms of L1 and L2 and hence the speed.
To see it clearly sketch it out.
 
  • #6
Aha! I follow. so it doesn't necessarily have to be the first harmonic, but they will definitely be in series? I've looked at it a little more and I think it's finally embedded itself into my brain. Thankyou for your help!
 

1. What is the relationship between the length of a pipe and the frequency of sound produced?

The length of a pipe is directly proportional to the frequency of sound produced. This means that as the length of the pipe increases, the frequency of the sound also increases.

2. How does the diameter of a pipe affect the frequency of sound produced?

The diameter of a pipe has an inverse relationship with the frequency of sound produced. This means that as the diameter of the pipe increases, the frequency of the sound decreases.

3. How does the material of a pipe impact the frequency of sound produced?

The material of a pipe has a minimal effect on the frequency of sound produced. However, denser materials tend to produce lower frequencies, while less dense materials produce higher frequencies.

4. How does the temperature of air inside a pipe affect the frequency of sound produced?

The temperature of air inside a pipe does not have a significant impact on the frequency of sound produced. However, at higher temperatures, the speed of sound increases, resulting in a slightly higher frequency of sound.

5. Can the frequency of sound in a pipe be altered by changing the air pressure inside?

Yes, the frequency of sound in a pipe can be altered by changing the air pressure inside. Higher air pressure results in a higher frequency of sound, while lower air pressure results in a lower frequency of sound.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
33
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Classical Physics
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
943
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top