# Standing waves on string with increasing tension

• echoi11
In summary, the conversation discusses the effect of tension on a standing wave on a string. It is determined that if tension is increased without changing the frequency, the standing wave will become a one-loop standing wave. The relationship between tension, velocity, wavelength, and frequency is also discussed, with the conclusion that increasing tension increases velocity and wavelength, but the number of loops in the standing wave remains constant. The frequency also changes depending on the mode of the standing wave.
echoi11
1. The problem statement, all variables, and given/known data
Consider a two-loop standing wave on a string. If we increase the tension without changing the frequency, what kind of standing wave can we obtain?
(a) one-loop (b) three-loop

## Homework Equations

Velocity = square root of(T/U)
Wavelength = velocity/ frequency.
f= 2L/(n)

## The Attempt at a Solution

I feel that this will become a one loop standing wave because if I plug in 2 in the frequency equation it becomes 2L. Also, it seems if you increase tension, you also increase velocity which increases wavelength, so does that mean it becomes a three loop standing wave instead. I am confused through the process.

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I had not hear the term "loop" before. I did some digging. It was as I had guessed. A loop is a half-wavelength, like this picture that I found:

If the number of loops stays constant, what happens to the frequency as tension increases? How are wavelength and frequency related?

echoi11 said:
if I plug in 2 in the frequency equation it becomes 2L.
echoi11 said:
if you increase tension, you also increase velocity which increases wavelength, so does that mean it becomes a three loop standing wave instead.
The overall length is fixed. How would increasing the length of each loop increase the number of loops?

I play a stringed instrument, so I can intuitively figure this out, from my experience. Try wrapping a rubber band around a pencil. Strum it and notice the pitch. If you can rotate the pencil, such that the length stays the same, and the tension increases, what happens when you strum it? Depending on the length of your band, you most likely will only be able to get one loop mode. If you have access to a guitar, you can try touching the string lightly with a finger in the middle, to create a two loop mode. You could try at 1/3 of the length of the string. What happens to the frequency, when you change modes, and the tension stays the same?

## 1. What is the relationship between tension and standing wave frequency?

As tension increases, the frequency of the standing wave also increases. This is because tension is directly proportional to the wave speed, and frequency is inversely proportional to the wave speed. Therefore, as tension increases, the wave speed increases, and the frequency increases as well.

## 2. How does changing the tension affect the amplitude of the standing wave?

Increasing tension will also increase the amplitude of the standing wave. This is because tension affects the energy of the wave, and a higher tension will result in a greater energy transfer, leading to a larger amplitude.

## 3. Is there a limit to how much tension can be applied before the string breaks?

Yes, there is a limit to the tension that can be applied before the string breaks. This is determined by the material and thickness of the string, and is known as the breaking tension. If the tension exceeds this limit, the string will break rather than continue to produce a standing wave.

## 4. How does the length of the string affect the standing wave with increasing tension?

The length of the string also plays a role in the standing wave with increasing tension. As the length of the string increases, the frequency of the standing wave decreases, while the wavelength increases. This is because the wavelength is inversely proportional to the frequency, and a longer string will have a longer wavelength, resulting in a lower frequency.

## 5. Can the standing wave pattern be altered by changing the tension?

Yes, the standing wave pattern can be altered by changing the tension. As tension increases, the number of nodes and antinodes in the standing wave will also increase. This can result in a different standing wave pattern, depending on the specific tension and length of the string.

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