Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time t =0 .The scale of the x axis is set by $x_{s} = 0.80 m$ .What is the amplitude of the wave?

The amplitude of the wave is 0.2 m

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The scale of the x axis = 0.80 m

Step 2: Understanding the concept of wave equation

The sinusoidal wave exhibits different displacements at different positions .Thus, the slope at different points varies with the position. We use this concept along with the equation of the travelling wave to calculate amplitude.

Formula:

The expression of wave equation, $y = y_{m} \cos (k x - ω t)$ (i)

The wavenumber of a wave, $k = \frac{2 π}{λ}$ (ii)

Here, $ω$ is the angular velocity of the wave and $y_{m}$ is the amplitude of the oscillation

Step 3: Calculation for the amplitude of the wave

The scale of x axis is given as 0.80 m. This distance is equivalent to two wavelengths.

Hence, the wavelength is given as:

$\begin{array}{l} 2 λ = 0.80 m \\ λ = 0.40 m \end{array}$

For x=0 and t=0 , equation (i) becomes-

$\begin{array}{l} y = y_{m} & \cos (k (0) - ω (0)) \\ y = y_{m} & \cos (0) \\ y = y_{m} \end{array}$

From the graph, the value of y at x =0 is 0.2 . So, the above equation becomes-

$y_{m} = 0.2$

Thus, the amplitude of the curve given in the graph is 0.2.

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Fundamentals Of Physics

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Short Answer

A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time t =0 .The scale of the x axis is set by $x_{s} = 0.80 m$ .What is the amplitude of the wave?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of wave equation

Step 3: Calculation for the amplitude of the wave

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A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time t =0 .The scale of the x axis is set by xs=0.80 m .What is the amplitude of the wave?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of wave equation

Step 3: Calculation for the amplitude of the wave

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A sinusoidal wave travels along a string under tension. Figure 16-31 gives the slopes along the string at time t =0 .The scale of the x axis is set by $x_{s} = 0.80 m$ .What is the amplitude of the wave?