# Wave on a string under tension

• BOYLANATOR
In summary, the conversation discusses a question about the length of a string and the equation for the third normal mode. The tension in the string is provided by a weight that is 100 times the mass of the string. The solution involves using the equations v=√(F/u) and u=m/L to determine the length of the string, which is found to be 9.8 meters. The conversation also mentions finding the amplitude of the equation y = A sin(3.pi.x/9.8)cos(30.pi.t), but is unsure how to do so.
BOYLANATOR

## Homework Statement

A pulse takes 0.1s to travel the length of a string. The tension in the string is provided by passing the string over a pulley to a weight which has 100 times the mass of the string.
What is the length (L) of the string?
What is the equation of the third normal mode.

v=√(F/u) u=m/L

## The Attempt at a Solution

We have L/t = √(100.m.g/(m/L) where g = surface gravity

So 100L^2 = 100gL
so L= magnitude(g) = 9.8 m

This type of question was not covered directly in our notes and I am unsure if my working is correct.
Thanks for any help.

Welcome to PF.
Reasoning seems fine to me - notice how the number end up all nice?
Did you do the next bit?

Last edited:
It was the simplicity in the final answer that made me doubt it.
Thank you, but what is LQ?

y_3 = (A_3)sin(n.pi.x/L)cos((w_n)t)

We have 1.5 waves in a time of 0.1s. So w = 30.pi radians
I don't see how I can get the amplitude.

So y = A sin(3.pi.x/9.8)cos(30.pi.t)

(where w is angular frequency)

but what is LQ?
A spelling mistake. Thanks.

angular frequency is radiens per second.
I don't see how I can get the amplitude.
me neither.
It was the simplicity in the final answer that made me doubt it.
I suppose with all the computer-randomized problems you get these days, nice numbers must be rare.

Note: cannot comment on answers as such - only methods and reasoning.

## 1. What is a wave on a string under tension?

A wave on a string under tension is a type of mechanical wave that occurs when a string or rope is stretched between two fixed points and then disturbed, causing a disturbance or pulse to travel along the string. The tension in the string allows the wave to propagate and maintain its shape.

## 2. How is the speed of a wave on a string under tension determined?

The speed of a wave on a string under tension is determined by the tension in the string and the string's mass per unit length. This relationship is described by the equation v = √(T/μ), where v is the speed of the wave, T is the tension in the string, and μ is the mass per unit length of the string.

## 3. What factors affect the amplitude and frequency of a wave on a string under tension?

The amplitude and frequency of a wave on a string under tension can be affected by the tension in the string, the length and mass of the string, and any external forces acting on the string. The amplitude of the wave is directly proportional to the initial disturbance or energy imparted to the string, while the frequency is inversely proportional to the length of the string.

## 4. How does the wavelength of a wave on a string under tension change with frequency?

The wavelength of a wave on a string under tension is inversely proportional to the frequency of the wave. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation λ = v/f, where λ is the wavelength, v is the speed of the wave, and f is the frequency.

## 5. How is the principle of superposition applied to waves on a string under tension?

The principle of superposition states that when two or more waves meet at a point, the resulting displacement is equal to the sum of the individual displacements. In the case of waves on a string under tension, this means that when two waves meet, their displacements will add together, resulting in a new wave with an amplitude that is the sum of the two individual wave amplitudes.

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