# Wave function for transverse waves on a rope

• arestes
In summary, the conversation discusses a problem from Serway's Physics for Scientists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19, which involves writing an expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction. The given characteristics are A = 8.00 cm, \lambda = 80.0 cm, f = 3.00 Hz, and y(0, t) = 0 at t = 0. Part (b) of the problem also asks for the expression for y when y(x, 0) = 0 at the point x = 10.0 cm.
arestes

## Homework Statement

Serway's Physics for Sciencetists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19:[/B]
(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope
in the negative x direction with the following characteristics:
A = 8.00 cm, $\lambda$= 80.0 cm, f = 3.00 Hz, and y(0, t) = 0 at t = 0. (b) What If? Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at the point x = 10.0 cm.

## Homework Equations

$$y(x,t)=ASin\left(kx\pm \omega t +\phi \right) \\k=\frac{2\pi}{\lambda} \\\omega=2\pi f$$
And the fact that the minus sign inside the Sine corresponds to a wave traveling along the +x direction and the plus sign to the -x direction.

## The Attempt at a Solution

k and $\omega$ are readily given by the formulas above. The direction of the wave chooses the right sign inside the Sine. Only problem is the initial phase $\phi$. Using the given data: at t=x=0 we must have:
$$Sin(\phi)=0$$ which, by trigonometry, corresponds to TWO solutions ( modulo 2 pi): Either $\phi=0$ or $\phi=\pi$ BUTthe solutions at the end of the book (odd numbered problems, Serway's Physics for Scientists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19, page 502, whose solution is given on page A-38 at the end of the book), gives only the first solution and says nothing about the second (with initial phase being pi).
Part (b) is just the same.

This cannot be discarded, I think. It fulfills all the given conditions, right? Am I missing something here? Does the direction of propagation of the wave influence on picking out only one of the two?
thanks

I agree with you.

thanks. But I'm surprisedd serway wouldn's say anything about the other solution. This problem's been there since at least the seventh edition

## 1. What is a wave function for transverse waves on a rope?

A wave function for transverse waves on a rope is a mathematical representation of the displacement of the rope at different points and times as the wave propagates through it. It describes the amplitude and wavelength of the wave and can be used to calculate the energy, velocity, and other properties of the wave.

## 2. How is the wave function for transverse waves on a rope derived?

The wave function for transverse waves on a rope is derived using the wave equation, which takes into account the tension in the rope, the density of the rope material, and the speed of the wave. The solution to this equation is a sine or cosine function, which represents the oscillatory nature of the transverse wave.

## 3. Can the wave function for transverse waves on a rope be used to predict the behavior of the wave?

Yes, the wave function for transverse waves on a rope can be used to predict the behavior of the wave. By plugging in different values for variables such as amplitude, wavelength, and time, we can determine the shape and motion of the wave at any given point in time.

## 4. How does the wave function for transverse waves on a rope relate to the superposition principle?

The wave function for transverse waves on a rope is based on the superposition principle, which states that the total displacement of a wave at a given point is the sum of the displacements from all individual waves passing through that point. This principle allows us to analyze the behavior of complex waves by breaking them down into simpler components.

## 5. Is the wave function for transverse waves on a rope affected by the properties of the rope material?

Yes, the wave function for transverse waves on a rope is affected by the properties of the rope material. The tension and density of the rope will determine the speed of the wave and how it propagates through the rope. Changes in these properties can result in changes to the wave function and the behavior of the transverse wave.

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