Calculating wave-length using path-length difference?

[wizzpowa]

Homework Statement

Hey guys, doing a lab in where we are analyzing a standing wave inside of a pipe. We recorded data points as we pulled out this tube where we saw the amplitude of the wave reach maximums and minimums (this was with using 2000 Hertz first and 1000 Hertz next)

In the analysis, it asks to " Using the data collected, calculate the
average wavelength of the sound waves using the
relationship for the path-length difference."

I know how to calculate wavelength normally, using the equation λ = V / F. But how can you find wave-length wit the 'path-length difference'? Thanks!

Homework Equations

λ = V / F.

The Attempt at a Solution

Confused, do not know how to approach the problem to solve for average wavelength

 

[wizzpowa]

also, I can give my data points for the max and min's of that is any help! :D

 

[haruspex]

The experiment gradually changes the length of the pipe, right? Do you know about harmonics in pipes, and how they relate to nodes, antinodes and wavelengths?

 

[mtayab1994]

also, I can give my data points for the max and min's of that is any help! :D

Well you have other equations such as V= λ/T where T is the period and from that you can conclude that V=λ*N where N is the frequency , and to me it looks like you did the experiment with 2 frequencies 2KHz and 1KHz. Count the wave length with both frequencies then add them up and divide by 2 to get your answer.

 

[wizzpowa]

haruspex: Correct, the length of the pipe gradually increased. I know that in the pipe, it's a standing wave, right? Since the frequency of the waves are the same. I know that when the waves are aligned it is constructive interference, and destructive interference on the flip side. I'm just confused on what exactly path length difference is, ( I know the definition but am still confused) and how you can relate it so you can solve for average wave length.

mtayab1994: what do you mean by "count the wave length?" It is asking me to find the wavelength, using the relationship for the path-length difference. The only variables I have are the frequencies, and the data we measured by increasing the distance of the pipe and recording the maximum and minimums. I just don't understand how these max and min points are helpful in finding the wave length through the path-length difference.

 

[mtayab1994]

haruspex: Correct, the length of the pipe gradually increased. I know that in the pipe, it's a standing wave, right? Since the frequency of the waves are the same. I know that when the waves are aligned it is constructive interference, and destructive interference on the flip side. I'm just confused on what exactly path length difference is, ( I know the definition but am still confused) and how you can relate it so you can solve for average wave length.

mtayab1994: what do you mean by "count the wave length?" It is asking me to find the wavelength, using the relationship for the path-length difference. The only variables I have are the frequencies, and the data we measured by increasing the distance of the pipe and recording the maximum and minimums. I just don't understand how these max and min points are helpful in finding the wave length through the path-length difference.

http://www.physicsclassroom.com/class/light/u12l3b.cfm

I think this should help you. Just read up on it.

 

[haruspex]

I know that in the pipe, it's a standing wave, right?

Yes, but think about the nodes and antinodes. Is the pipe open or closed at the ends, or one of each? What can a standing wave in it look like? What does that mean about the possible number of wavelengths (could include a fraction) in the standing wave when the pipe resonates?