Speed and Frequency of Waves Lab

[member 529879]

I recently had a lab in physics class that I was a little confused about. I posted a picture of a couple parts of the lab including the instructions and a couple of questions. I also highlighted a few things that confused me. In the instructions it said that all objects vibrate at a set of natural frequencies. What does it mean by set? I thought each object only had one natural frequency. I was also confused by the statement that ressonace occurring increased the volume. I would think that resonance would result in more sound, but not sound with a greater amplitude. Finally can somebody explain the last things I highlighted and explain the two questions at the bottom of the attached image?

 

[CWatters]

..set of natural frequencies. What does it mean by set?

In this case they mean the harmonics. In other problems they might mean vibrations in different planes (eg. x,y,z axis or torsion).

I was also confused by the statement that ressonace occurring increased the volume.

When you blow across the top of a bottle energy is transferred from the source (you) into the vibrating air column. It's possible to prove mathematically that this energy is transferred most efficiently if it's applied at the resonant frequency. Have you ever pushed some one on a children's swing? Try pushing them at various frequencies and you will find they go higher if you push them at "just the right frequency" aka the resonant frequency. If you tried to make them swing much faster (say 10Hz) what would happen?

I would think that resonance would result in more sound, but not sound with a greater amplitude.

What do you mean by "more" sound? A louder sound has a greater amplitude.

 

[CWatters]

You also highlighted...

because the set up measures odd harmonics you will only get resonance at 1/4L and 3/4L

See the diagram in your post. It's not obvious from the diagram but the air molecules in the pipe actually vibrate horizontally left to right not vertically. The curved lines show the amplitude of the vibration at various points along the pipe (eg this is nothing like a guitar string. On a guitar string the molecules do vibrate vertically).

There are some rules to remember...

1) The pipe is closed at the right hand end so the air right next to that end cannot easily vibrate horizontally. This means there is a node at a closed end.

2) The pipe is open at the left hand end so the air next to that can vibrate horizontally. This means there is an anti-node at an open end.

Look at each of the four diagrams and you will see that they show four different ways how these two rules can be met. In each case the wave length is different...

In the first diagram only a quarter of a whole wave fits in the pipe. So the length of the pipe is the 1/4 * wave length or L = λ/4.

In the second diagram only three quarters of a whole wave fits in. So the length of the pipe is 3/4 * wave length or L=3λ/4

etc etc.

Note that it won't resonate at (for example) L = λ because that would imply a node at both ends.

 

[CWatters]

As an exercise perhaps try making the same drawings for a flute which is a tube open at both ends.

 

[CWatters]

I've given you quite a lot of help and info above. Try and answer the two questions on the sheet yourself. If you post an attempt we'll tell you if it's right.

 

[andrevdh]

http://www.physicscentral.com/experiment/physicsathome/pasta-resonance.cfm

 

[member 529879]

Thanks for the responses. Would the answer to the first question be yes, because the frequency of the tuning fork matches one of the resonant frequencies of the tube? Also how would I even start the second question? Sorry that I'm asking a lot of questions I missed a day or two of class.

 

[CWatters]

Hint: What is the frequency range that the human ear can detect?

 

[member 529879]

This might be way off, but would the answer to number two be 9/4 of a wavelength?

 

[andrevdh]

The fifth harmonic? It is a bit difficult to read the image due to the low resolution.
You will need to use your data to determine this because the speed is temperature dependent.
At the formation of the first standing wave we get 1/4 λ. This is called the 1st harmonic or fundamental.
At the formation of the 2nd standing wave we get 3/4 λ. This is called the 3rd harmonic...
Usually the length is fixed and the frequency is changed so that the tube will resonate at different frequencies, but in this experiment the frequency is kept the same and the length is changed to accommodate it. The tube
then resonates when the standing wave is formed at these particular lengths.

 

[CWatters]

This might be way off, but would the answer to number two be 9/4 of a wavelength?

Yes but I believe they want the length in meters.

Best answer Q1 first. A relevant equation would be V = f*λ

 

[member 529879]

I think my problem is I don't really understand resonance and natural frequency vey well. Do most objects have more than one natural frequency, and if so what determines which of its natural frequencies it vibrates at? Why must one end of the tube have a node while the other has an antinode? I also saw a video on a lab similar to this one that said something about the sound somehow being amplified by a standing wave be created, did I understand that correctly?

 

[CWatters]

I think my problem is I don't really understand resonance and natural frequency vey well. Do most objects have more than one natural frequency, and if so what determines which of its natural frequencies it vibrates at?

Yes many objects will resonate at more than one frequency. Usually these frequencies are related to some fraction or multiple of a dimension such as the length. The source or driver usually determines which frequency it actually vibrates at. Consider an adult pushing a child on a swing. The adult can try an push the swing at any frequency. The frequency(ies) they find easiest to push at depends on the natural frequency(ies) of the child/swing.

Why must one end of the tube have a node while the other has an antinode?

See post #3 where I tried to explain that. What you get at the ends depends if it's open or closed. If it's closed the air next to the closed end finds it hard to move because it's constrained by the end wall - so you get a node which is a point of minimum amplitude. In your example you have one open and one closed end so at resonance you get a node at one and an antinode at the other. A flute is closed at both ends so there is a node at both ends.

I also saw a video on a lab similar to this one that said something about the sound somehow being amplified by a standing wave be created, did I understand that correctly?

Yes. At a resonant frequency the maximum amount of energy is transferred from the driver/source to the load (the vibrating air column). For example its very hard to make a child on a swing oscillate at high frequencies (say 10 Hz). It's much easier to push the child at his natural frequency and make the swing go higher and higher. Height of a swing is equivalent to amplitude or loudness in the case of an experiment involving sound.