Help with physics resonance

[dekoi]

There's a metal cylinder from which water is flowing out at a rate of 10^-6 m^3/s. A tuning fork of 300 Hz is placed on top of the cylinder. At what water levels will the first two resonance frequencies be heard?

It doesn't seem like a difficult problem, and it really isn't. I just can't seem to see it.

I don't think the flow rate has any signifiance in calculation; it's only useful to know that the water level is decreasing.

It's an open-closed system, so the natural frequencies are $$f_n = \frac{nv}{4L}$$ where n = 1, 3, 5, 7...

So in the first case, i think the first frequency heard would be 300 Hz. Hence, one can solve for $$L_1$$ to attain 0.286m. But how about for the next? Will it just be 3 times L_1 ? Or how do you solve for it otherwise?Thanks
-----------------------------

Question 2: Is it logical to ask whether the beat frequency is e.g. +4 or -4? Afterall, $$f_{beat} = |f_2 - f_1|$$ so because of the absolute value,it is always +4.

 

[dekoi]

Anyone?


.

 

[kyle8921]

As a scientist, it is important to always question and analyze the information presented to us. In this case, it is important to clarify the context of the problem and what is being asked.

If the beat frequency is defined as the absolute value of the difference between two frequencies, then it would always be a positive value. However, if the problem is asking for the direction of the beat frequency (whether it is increasing or decreasing), then it would be logical to consider both positive and negative values.

It is also important to note that in certain situations, the beat frequency can be negative. For example, if the two frequencies are very close together and one is slightly higher than the other, the beat frequency can be negative. This is because the two waves are out of phase and their interference results in a lower amplitude.

In conclusion, it is important to clarify the context and definition of the beat frequency in order to determine whether it can be positive or negative.