Tapping a cup to produce sound above and below water

[manofdemon]

Homework Statement

The task is to investigate and explain why the sound produced when you tap a cup on its base (whilst its upside down) changes, when the cup is above water, on the surface of the water, and below water.

I am not sure of the theory, although when I carried out the experiment, the noise was deeper when tapped on the surface, then even deeper when tapped below water.

Can somebody please push me in the right direction toward relevant theory explaining this?

Cheers

 

[manofdemon]

in my own research, i have learned that sound travels faster in water.

i have found the formula speed = frequency * wavelength

which gives frequency = speed / wavelength

okay so for an experiment, i have to tap these cups and so i think ill be using this formula to verify or compare with results
however I am unsure how to find the wavelength to use in the formula so that i can find frequency

 

[ehild]

Tapping the cup will make a noise and the air inside the cap will resonate to that frequency which produces standing waves in its volume, filled with air in the first two cases, and with water in the third case. Try to imagine those standing waves. You can consider that cap a cylinder.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html#c3

ehild

 

[manofdemon]

Tapping the cup will make a noise and the air inside the cap will resonate to that frequency which produces standing waves in its volume, filled with air in the first two cases, and with water in the third case. Try to imagine those standing waves. You can consider that cap a cylinder.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html#c3

ehild

will the change from an open end standing wave to a closed end (ie. using the water to block the open end of the cup) change the frequency of the sound?

thanks for ur reply

 

[ehild]

will the change from an open end standing wave to a closed end (ie. using the water to block the open end of the cup) change the frequency of the sound?

thanks for ur reply

Closing or opening the end does not change the frequency of any sound: it is a different sound made by the cup if it is closed or open. The wavelenghts of the standing waves set-up in open-end cup are different from those in a closed-end one. You know that frequency=speed/ wavelength . So the frequencies are different, too.


ehild

 

[ZXY123]

Closing or opening the end does not change the frequency of any sound: it is a different sound made by the cup if it is closed or open. The wavelenghts of the standing waves set-up in open-end cup are different from those in a closed-end one. You know that frequency=speed/ wavelength . So the frequencies are different, too.


ehild

How would the frequencies be different when Closing or opening the end ?How are the standing waves formed different ?My research showed that air cannot vibrate when the two ends of a pipe containing air are both closed,does it mean standing waves cannot form in those kind of pipe.

 

[ehild]

You know that there is a node of the standing wave pattern at a closed end and there is an anti-node at the open end. The end where you generate the sound is also an anti-node. Tapping the base of the cup makes it vibrate and the vibration is transferred to the air molecules inside the cup. The vibration generated in the cup contains a couple of frequencies. These vibrations travel in the air inside the cup with the speed of sound. There are some frequencies for which the cup resonates: stationary standing waves can form. If the cup is entirely in air, there are anti-nodes at both ends, so the length of the cup is integer multiple of the half wavelength. If the opening of the cup is immersed into water, the vibration of air molecules can not make the water molecules also vibrate with the same amplitude, because of the strong interaction among water molecules. So only such standing waves can form which have a node at the water surface. The length of the cup is odd multiple of a quarter wavelength. I am not sure what happens when the cup is immersed below the water. Sometimes I got a deeper sound, sometimes a higher one. In this case,you tap the base under water, it generates sound inside the water, so the opening of the cup should be an antinode. But you might hear the sound according to the standing waves inside the water and if you do the experiment in a bathtube it is really deep :)

ehild

 

[ZXY123]

Thanks for your kind help,but i still have some other questions.Hope you can help .

The vibration generated in the cup contains a couple of frequencies. These vibrations travel in the air inside the cup with the speed of sound. There are some frequencies for which the cup resonates: stationary standing waves can form.ehild

(1)SO it is that there must be standing waves in the cup when it is above water and on water?from the formulas of standing waves ,i derived that the frequency of standing waves above water is lower than that on water,is it true?
(2)And for below water,should the bottom of the cup be below water?Will the water resistance affect the sound produced?Or it is that below water refers to part of the cup is inside water?
(3) for part of the cup inside the water ,how will the depth of cup inside water affect the sound produced? THanks a lot:)

 

[ehild]

This problem is about a rather complicated thing, so I do not know the answers for sure.
Any solid body will produce sound if you tap it. But the cup is hollow and the air inside resonates to some of the vibrations of the wall and standing waves can form. You have a stronger and less noise-like sound if there are standing waves.
The fundamental mode of a cylinder open at both ends is a half-wave, as there are anti-nodes at both ends and a node in the middle.
If one end is closed and the other is open, the fundamental mode is a quarter wave. The length of the cylinder is the same, so which frequency is higher?
But it is possible that this frequency is too low, and the generating vibration does not contain it. Then it is possible that the standing wave has two nodes and two anti-nodes, that is the length of the cylinder is equal to 3/4 wavelength.
When I tried it with my cup it sounded definitely deeper when the opening of the cup touched the water surface, so I got the fundamental mode, I guess.

I understand the third question that the whole cup is under water. but I do not know the answer. When trying with a metal cup, the sound was deeper. With glass, it was the same as in case when only the opening was under the water.

ehild

 

[ZXY123]

"But it is possible that this frequency is too low, and the generating vibration does not contain it. Then it is possible that the standing wave has two nodes and two anti-nodes, that is the length of the cylinder is equal to 3/4 wavelength. "


ehild

Sorry i cannot quite get your meaning ,do you mean that the one above water is 3/4 wavelenth and the one on water is 1/2 wavelength ,so that the one above water has higher frequency ?Then what does the wavelength of the sound depend on?

 

[ehild]

No, I mean 1/2wavelength above water and 1/4 wavelength on water as the fundamental modes.

ehild

 

[ZXY123]

thanks a lot

 

[tiny-tim]

hi manofdemon!

… the noise was deeper when tapped on the surface, then even deeper when tapped below water.

when the open end of the cup is pushed further below water, the pressure on the air inside the cup changes, and so either the volume of the air or its temperature (or both) must also change …

which of those three (pressure volume and temperature) does the frequency depend on?

you need to make experiments to find out (possibly with different-sized cups)