Understanding Sound Waves: Measuring Speed and Wavelength

[Nikitin]

Hi guys, I have problems with a high-school assignment:

Homework Statement

http://img843.imageshack.us/img843/3748/74698735.png
An experimenter tries to determine the speed of sound in air. He tries to lower and elevate the water in the tube at the same time as he hits on the fork, until he hears an increase of the tone. He marks the spot with A. He repeats the same thing and finds a new spot. He marks it "B". The fork has a movement frequency f=440hz.


1) Determine why the air in the tube sends out sound of the same frequency as f?
2) Explain that the distance AB is half the wavelength of the sound-wave in the air.
3) Calculate the speed of sound in air.

Homework Equations

v=f*[lambda]

The Attempt at a Solution

1) Because the fork vibrates at 440 hz, thus it must send out 440 complete sound waves per second down the tube. Correct?
2) OK, here is the tricky question. I know that the water reflects the sound waves, and at point A & B the reflected sound waves and the incoming soundwaves interfere, thus increasing the amplitude and increasing the tone of the new wave (new wave = incoming wave + reflected wave).

I am finding it extremely hard to prove that distance AB = 0.5*[lambda]
3) No problem. v=f*2*(AB) This part is pretty easy.

Any help is highly appreciated..

 

[L-x]

Are you sure that interference always increases the amplitude?

 

[Nikitin]

no, but if it matches the frequency of the other wave and creates resonance (which it does in the post)..

 

[L-x]

Why does the experimenter only hear the increase in amplitude when the water is at certain heights?

Edit: it might help to try to draw the sound wave inside the tube.

 

[Nikitin]

Because that is when the reflected sound waves from the water start to resonance with the incoming waves from the fork?

So if the water level is a bit too high or a bit too low the entire thing gets out of sync and we won't see an increase in tone?

I'l try drawing them sound waves in the tube

 

[L-x]

So if the water level is too high or too low the entire thing gets out of sync and we won't see an increase in tone?

Bingo. Two waves will only interfere constructively (in a way which results in an increase in amplitude) if they are in phase.

When the column of air inside the tube is resonating, its length is such that the incident and reflected sound waves are in phase with each other.

Edit:
Look at this diagram once you've had a go at drawing the sound waves yourself, try to imagine what the drawing would look like if the water level was somewhere between A and B
http://image.wistatutor.com/content/waves/resonance-end-correction.gif

 

[Nikitin]

Hm, but the amplitude would increase even if the wave-front collisions are not perfect (let's say a sound-wave front of high pressure hits a sound-wave front which borders between low and high pressure but is mostly high pressure).. Right?

I will study your link, hopefully I can solve the second problem with its help.

 

[Nikitin]

OK, I sat down and started thinking. I believe I got it now kind-of, but I am still wondering about the question abovealso: those signs on the right, representing the actual sound-wave, aren't they a bit badly drawn? Shouldn't the sound-wave be made up of ONLY of high-pressure to low pressure waves, instead of just a low-pressure wave representing the negative part of the wave and a high-pressure wave representing the wave-top?

 

[L-x]

The amplitude of the sum wave would indeed still increase if the waves were a little out of phase, however it will be greatest when they are exactly in phase, and will decrease as they get more out of phase until eventually it reaches 0 (at this point the waves are exactly out of phase).

As a result of this the sound will be more audible the closer the waves are to being exactly in phase, and as it happens because of how resonance works (think feedback loops), the amplitude of the sound will actually fall away very quickly as the waves inside the tube become out of phase.

You can ignore most of the diagram (the stripes on the side are, incidentally, another way of representing the wave, look at the pattern of their closeness and how it is related to the amplitude of the standing wave inside the tube), i just wanted to provide a general clue about the shape of the waves.

Edit:
Yes they are poorly drawn, my best guess is that at some point the picture was resized, which led to be the "stipes" becoming rather unhelpful

 

[Nikitin]

Hi. We have only learned about the transverse waves and the longitudinal waves and using sine to represent periodical movements and regular graphs to represent the power of longitudinal waves. About the soundwave, we haven't been thought the models (like the ones used in this link http://www.asc-csa.gc.ca/images/neemo_open_tube_t.gif ) used in your picture.

PS. sry for my english.

exactly what are these red lines representing? http://en.wikipedia.org/wiki/File:OpenCylinderResonance.svg

 

[Nikitin]

Bump? This should be a pretty simple question.. I believe these lines are a function for the increase and decrease of air pressure, but I would appreciate a proper explanation of them in this http://image.wistatutor.com/content/waves/resonance-end-correction.gif picture

both of the waves at example 2 are having their positive peak, right?

EDIT: I think I see now why it is 1/2. It is obvious that the reflection of the line would be imperfect, and thus the two halves of the tube wouldn't be symmetrical. I'l take a look at this tomorrow (hope someone can post a complete explanation.. I would rly appreciate it!).

Anyway, thank you L-x, your help really put me to the right track. Anyway I'm off to chat with m8's.