For this question we have a string over a pulley tied to a mass, and the other s

Question

For this question we have a string over a pulley tied to a mass, and the other side is attached to a vibrating source.

Answers are... (increase, decrease, or stay the same) I have a general idea but want to verify my answers...

We are supposed to determine if we change the length/tension what will happen to the other noted items.

The answers I have are listed, I am pretty sure about the last two rows, and the first two rows. However, I'm unsure about how the wavelength and fundamental frequency would change. It almost seems like if the number of antinodes increases, the wavelenth should be opposite (since you have the same length of string but more cycles?) unsure about this.. any explanations/critique is greatly appreciated.

Explanation / Answer

In a string, there is a difference between wavelength and fundamental wavelength. Fundamental wavelenth of first order is when there is one antinode which means wavelength is twice the length of the string. Thus, your answers about fundamental wavelength are absolutely spot on.

So going by the formula, v = (TL/m) where T is tension, L is length and m is mass of string, we get

f =   (TL/m) But at fundamental frequency and wavelength, = 2L.

Thus, fundamental frequency = [ (TL/m) ]/2L = (T/4mL).

Hence, when length is increased, fundamental frequency decreases and vice versa. Opposutte for Tension. So again, your answers are spot on.

However, when we talk about wavelength ONLY (not fundamental wavelength), it is unaffected by tension or length. It affects only the velocity and subsequently the frequency. However, the wavelength which depends on how far apart the nodes and antinodes are will remain unaffected. Since v = f, if Tension increases, velocity will increase and hence, frequency will increase. However, will remain the same.

Hope this helps. Do let me know if I was right:)

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