Sound generated when a cup of water is hit

[nairsgame]

Hello

I have some questions regarding the following problem:

Imagine I have a glass beaker partially filled with water. Assume that I were to hit the beaker (say at the top edge to be specific) with a noodle stick. Assume that I do not hit again until the vibrations have completely died down.

Question#1: Will the frequency of the sound generated be the same every time? Or does it vary with the force with which I hit?

Question#2: If the frequency in #1 were to remain same always, Can I consider this as the natural frequency of that system?

Question#3: Assume that I were to change the density of the liquid (but keep the length of the air column above it same). Can the frequency be different from above? Or will only the amplitude change due to damping?

Thanks
Game

 

[Bobbywhy]

nairsgame, Welcome to Physics Forums!

Please see this thread from last January. I think it contains answers to all your questions.

https://www.physicsforums.com/showthread.php?t=569858

Cheers,
Bobbywhy

 

[nairsgame]

Thank you Bobbywhy!

That answers my question

Thanks
Game

 

[nairsgame]

I have some more question on this:

1. when I hit an empty cup, is the cup's surface vibrating at a different frequency compared to the air column inside the cup? If so, will I be able to detect 2 sets of frequency one inside the cup and another outside the cup along it's sides?

2. When I fill it partially with water, does part of the cup above the water level vibrate at a different frequency than one below it? Or does water just dampens the vibration and not alter the vibrating characteristics of the cup?

3. When I partially fill the cup with water, like in Q#1 above, will I be able to detect 3 different frequencies ?

4. Does a partially filled cup actually work somewhat similar to a stringed instrument? i.e. does the water surface act similar to how we vary the length of the string in a stringed instrument when held lightly

Thanks
Game

 

[Alkim]

The sound you hear is basically generated by the cup's wall which can move freely and exactly as in the case of a string instrument its frequency depends on the length vibrating. The liquid of course vibrates too (as well as your finger pressing the string of a violine) but it does not affect too much the sound. The sound is actually a superposition of different frequencies and this defines its characteristic "timber". The frequency composition can be analyzed by Fourier transforming the waveform. The strength with which you hit the glass generally does not affect too much the main frequency but it does change the relationship between the amplitudes of the different frequencies and therefore it affects the timber (check it yourself next time you are having a glass of wine).