How can sound move faster one pipe than another? (TBR ex., NOT a test question)

[Gauss44]

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TBR
Example 6.4a.
In studying the relationship between the variable lengths of two open resonating pipes and the number of harmonics each pipe can produce at different lengths, a musicologist notices the following trends in her data:

A graph compares pipe A to pipe B. Pipe A is 2meters long and has 4 nodes, while pipe B is 3 meters long and has 4 nodes. On a graph of nodes versus length, pipe A has a steeper slope.

Question: Pipes A and B are both telescoping pipes. What could explain the difference in slope for the lines representing each pipe?

Correct answer: The speed of sound is slower for pipe A than for pipe B.

Me: I get that n=2Lfn/v. But I don't get the concept. How can sound travel at different speeds in the same medium, air???

 

[onedirection]

v = f*lambda

They are traveling at the same frequencies because both have 4 nodes

But the pipe A is shorter than pipe B; therefore wavelength is shorter [same # of nodes shorter in less length] making velocity less

That's the best I can come up with; I typically don't think of wavelength having too much of an influence on things with pipes

but I guess it can here? can someone confirm

 

[enervate]

A graph compares pipe A to pipe B. Pipe A is 2meters long and has 4 nodes, while pipe B is 3 meters long and has 4 nodes. On a graph of nodes versus length, pipe A has a steeper slope.

Question: Pipes A and B are both telescoping pipes. What could explain the difference in slope for the lines representing each pipe?

Correct answer: The speed of sound is slower for pipe A than for pipe B.

Me: I get that n=2Lfn/v. But I don't get the concept. How can sound travel at different speeds in the same medium, air???

What page is this on? I don't remember seeing it in my book.

Anyway, consider each node to be half a wavelength. That means L/n = 0.5 * lambda and 2(L/n) = lambda.

L_A = 2 m and n_B = 4 so lambda_A = (2/4)*2 = 1 m.

L_B = 3 m and n_B = 4 so lambda_B = (3/4)*2 = 1.5 m.

Now, v = f * lambda and, since the widths of the pipes are the same, the frequencies are the same for both pipes. That leaves v = constant * lambda. Obviously L_B > L_A so v_B > v_A.

 

[Gauss44]

What page is this on? I don't remember seeing it in my book.

Anyway, consider each node to be half a wavelength. That means L/n = 0.5 * lambda and 2(L/n) = lambda.

L_A = 2 m and n_B = 4 so lambda_A = (2/4)*2 = 1 m.

L_B = 3 m and n_B = 4 so lambda_B = (3/4)*2 = 1.5 m.

Now, v = f * lambda and, since the widths of the pipes are the same, the frequencies are the same for both pipes. That leaves v = constant * lambda. Obviously L_B > L_A so v_B > v_A.

Page 18 of my book, last copyrighted in 2008. It's on the very last page of the Sound chapter before the chapter practice exams.

Now that someone mentioned the frequencies remain the same, I might get it. I'm visualizing this: In a fixed amount of time, say .002 seconds, sound travels exactly one wavelength in both pipes, even though one wavelength is larger than the other.

 

[HesitantManatee]

Me: I get that n=2Lfn/v. But I don't get the concept. How can sound travel at different speeds in the same medium, air???

The speed of a wave is more or less always the same in a given medium. However the question doesn't state that both pipes are in the same medium. It only ask you to give a situation that fits the data.

 

[onedirection]

The speed of a wave is more or less always the same in a given medium. However the question doesn't state that both pipes are in the same medium. It only ask you to give a situation that fits the data.

I haven't read the question yet/seen the passage

but I like that answer better than the wavelength being different because from what I remember wavelength really has no influence on these types of questions, it's basically the medium that's the important thing

 

[gettheleadout]

Haha I remember this example question, I didn't understand it and I still don't.

😛

 

[enervate]

After returning to this question in the workbook, I agree that it is very weird but the concept it must incorporate is clear. Very strange.

 

[FeinMS]

The same medium doesn't necessarily mean same speed. Temperature can affect the speed of the sound in the same medium. For example, sound travels faster in hot air than cold air.

 

[gettheleadout]

The same medium doesn't necessarily mean same speed. Temperature can affect the speed of the sound in the same medium. For example, sound travels faster in hot air than cold air.

Right, but that's irrelevant in the context of this question.

 

[enervate]

Maybe the pipes themselves are made out of different materials?

 

[wjs010]

I thought it only depended on the medium? Ie, Sound travels faster In water than air. What if one pipe is in air and the other is in water? Then the one in water travels a greater speed. Someone please come up with an answer to this annoying question. Lol

 

[benjaminl1nus]

Your question is how can sound travel different speeds in the same medium, right?

Well, the way I see it is...

So sound travels faster in a solid than a liquid for a given compound. this is because the intermolecular forces between molecules are stronger for a solid than for a liquid. stronger intermolecular forces means a greater restoring force and therefore a faster propagation of the wave.

in warm air, molecules are traveling faster than they would be compared to cooler air. warmer air is, by the ideal gas law, characterized by greater pressure. this makes sense because the faster molecules move, the more often they collide on a given area, producing a higher than normal pressure.

warmer air --> greater pressure --> greater restoring force (pressure is proportional to Force for a given area)--> faster wave propagation.

Does this make sense?

 

[sillyjoe]

Right, but that's irrelevant in the context of this question.

Any luck in making sense of this problem? How are they relating the slope here using the equation to show their answer?

 

[DrknoSDN]

Any luck in making sense of this problem? How are they relating the slope here using the equation to show their answer?

Sometimes it's best to realize the authors can write bad (poorly understood) questions. The answer is not wrong under narrow but possible circumstances.

The question is talking about musical instruments, and the answer provided says the speed of sound is different in each pipe given equal lengths...

One very plausible explanation is that the pressure inside one instrument is greater than in the other. It should be widely understood that pressure changes sound propagation speed based on molecular kinetics. The faster speed pipe (instrument) might just require a lot more pressure to produce a tone, so the speed of sound within the instruments will be different.
Speed of sound at various pressures/elevations: http://www.engineeringtoolbox.com/elevation-speed-sound-air-d_1534.html

 

[gettheleadout]

Sometimes it's best to realize the authors can write bad (poorly understood) questions. The answer is not wrong under narrow but possible circumstances.

The question is talking about musical instruments, and the answer provided says the speed of sound is different in each pipe given equal lengths...

One very plausible explanation is that the pressure inside one instrument is greater than in the other. It should be widely understood that pressure changes sound propagation speed based on molecular kinetics. The faster speed pipe (instrument) might just require a lot more pressure to produce a tone, so the speed of sound within the instruments will be different.
Speed of sound at various pressures/elevations: http://www.engineeringtoolbox.com/elevation-speed-sound-air-d_1534.html

If the question had stated that the pipes were components of wind instruments and that the harmonics observed were produced while the instruments were being played, I would be much more open to considering this reasoning acceptable to expect from a test taker. As it is, the question makes no mention of air flow through the pipes. Your reasoning is correct, but I still won't defend this question lol.

 

[sillyjoe]

Mathematically are they just using the equation nv/2l and since the slope increases (n/L) then the velocity of the wave in the pipe decreases?

 

[DrknoSDN]

If the question had stated that the pipes were components of wind instruments and that the harmonics observed were produced while the instruments were being played, I would be much more open to considering this reasoning acceptable to expect from a test taker. As it is, the question makes no mention of air flow through the pipes. Your reasoning is correct, but I still won't defend this question lol.

It's a pipe based musical instrument that requires flow of air through it. Could it be anything other than a wind instrument? (Not sarcastic, I am not familiar with orchestral instruments)

Edit: This question is not the greatest, making you go against things that are usually assumed to be true. (Velocity of sound in a medium is a constant, given identical conditions)

 

[gettheleadout]

It's a pipe based musical instrument that requires flow of air through it. Could it be anything other than a wind instrument? (Not sarcastic, I am not familiar with orchestral instruments)

Edit: This question is not the greatest, making you go against things that are usually assumed to be true. (Velocity of sound in a medium is a constant, given identical conditions)

All the question stem says is "two open resonating pipes." To me, assuming that air flow is required is unjustified. The pipes could each just have one open end near a sound source.