Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Four waves are to be sent along the same string, in the same direction:

$y_{1} (x, t) = (4.00 mm) \sin (2 πx - 400 πt) y_{2} (x, t) = (4.00 m m) s i n (2 π x - 400 π t + 0.7 π) y_{3} (x, t) = (4.00 m m) s i n (2 π x - 400 π t + π) y_{4} (x, t) = (4.00 m m) s i n (2 π x - 400 π t + 1.7 π)$
What is the amplitude of the resultant wave?

There is no resultant wave. Hence the amplitude is zero.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

$i . y_{1} (x, t) = (4.00 mm) \sin (2 πx - 400 πt) ii . y_{1} (x, t) = (4.00 mm) \sin (2 πx - 400 πt + 0.7 π) iii . y_{1} (x, t) = (4.00 mm) \sin (2 πx - 400 πt + π) iv . y_{1} (x, t) = (4.00 mm) \sin (2 πx - 400 πt + 1.7 π)$

Step 2: Understanding the concept of superposition principle

Using the principle of superposition of the waves, we can find the amplitude of the resultant wave. We can also observe the phase difference between the waves to determine their resultant wave.

Step 3: Calculation of the amplitude of the wave

From the given wave equations, we can observe that all the waves are traveling along the same direction. However, the phase difference between the 1^st and 3^rdwave is $π$ , therefore, there would be no resulting wave from the superposition of these two waves. Similarly, it can be observed that the 2^nd and 4^th wave have phase difference equals to $π$ . Therefore, again, there would be no resulting wave from superposition of these two waves. Hence, we can conclude that, there would be no wave generated as a resultant of the superposition of these four waves.

So the amplitude of the resulting wave would be zero.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of superposition principle

Step 3: Calculation of the amplitude of the wave

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Fundamentals Of Physics

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Short Answer

Four waves are to be sent along the same string, in the same direction: y1(x,t)=(4.00mm)sin(2πx-400πt)y2(x,t)=(4.00mm)sin(2πx-400πt+0.7π)y3(x,t)=(4.00mm)sin(2πx-400πt+π)y4(x,t)=(4.00mm)sin(2πx-400πt+1.7π)What is the amplitude of the resultant wave?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of superposition principle

Step 3: Calculation of the amplitude of the wave

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