# Tonometer experiment

1. Nov 25, 2009

### Shing

Today, in my school's physics lab lecture, we were doing an experiment for Standing wave. And
I found a strange phenomenon:
If I made the distance between tonometer and the pulley long eough, there won't be any observed standing wave!! I have no idea the reason. First, I thought: um..... because the tension will larger when the length larger? then I find the tension will always be mg! (is it true?)
Then I have thought up a few reason, no idea how to find out whether they are right or not.

1.) because there is elasticity for the rope, the longer the length is, the more it adsorbs. (but how to disprove that if it is wrong? and how could all the vibration , say out of the blue, disappear to a degree that we can't observe the vibration ?)

2.) vibration will make the tension not a constant neither parallel to the table, and the
tension canceled the movement (but that can't explain why when it was short enough, we did observe the standing wave.)

would anyone be kind enough to give me a few hints or keys?

So I have no idea the reason. Sorry for the poor writing (english is my second language)and manner of asking. Thanks for reading =)

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2. Nov 28, 2009

### wywong

If you do not apply a steady vibration but apply a short pulse train (e.g. turning on the electricity only momentarily) instead, you can observe the pulse train travels along the string and bounces back. You should also notice that its amplitude attenuates as it travels. That is caused by absorption by the string as well air drag. For standing wave to occur, the reflected wave and the forward wave should be of comparable amplitudes. As the length of the string increases, the amplitude difference increases and the envelop of the standing wave gradually (not out of the blue) changes from a sine curve to a straight line.

Wai Wong

3. Nov 29, 2009

### Shing

But I also observed that the tonometer's vibration became weaker when there was not any observed Standing wave? So that means tension will NOT always by mg?
Besides, yeah, it is more likely that the envelop of the standing wave gradually (not out of the blue) changes from a sine curve to a straight line. But it should be also within a small change of length (~0.05m)

4. Nov 29, 2009

### wywong

The tension along any light string must be constant, or else some part of it will have very large acceleration (a=F/m). In your case, the weight of the string should indeed be small compared with mg so the tension should be mg throughout. Of course the string tension varies when it vibrates, but the change is small and the average tension is still mg.

The vibration you measure is the sum of the vibration source plus the reflection of all previous vibrations (note that a wave can reflect more than once before dying down). If the attenuation of the string is large you only get the vibration of the source. If the attenuation is small, you can get a measurement many times as strong.

When you talk about a change as small as 0.05m, I think the loss of standing wave is caused by destructive interference - the length of string being not whole number of half wavelengths. That is not the attenuation we are talking about. If you change the string length from say 10 wavelengths to 15, 20, 25, 30, ... and so on, you will observe the gradual change in the envelop.

Wai Wong