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A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m traveling in the...

Question:

A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m traveling in the same direction. What are (a) the largest and (b) the smallest resultant amplitudes that can occur, and under what conditions will these maxima and minima arise?

Superposition of Waves

When to waves superpose with each other they form a new wave that is the result of both the waves and the resultant amplitude of the new wave is the vector sum of the amplitudes of both the waves. The constructive pattern amplitudes gets added and for destructive pattern, amplitudes get subtracted.

Answer and Explanation:

Data Given

  • Amplitude of wave one {eq}y_1 = 0.30 \ \rm m {/eq}
  • The amplitude of wave two {eq}y_2 = 0.20 \ \rm m {/eq}

Part A) The resultant of the two waves will be largest when two waves superpose constructively means crust of one wave fall on the crust of the another wave

{eq}\begin{align} y_{max} = y_1 + y_2 \end{align} {/eq}

{eq}\begin{align} y_{max} = 0.30 \ \rm m + 0.20 \ \rm m \end{align} {/eq}

{eq}\begin{align} \color{blue}{\boxed{ y_{max} = 0.50 \ \rm m}} \end{align} {/eq}


Part B)The resultant of the two waves will be smallest when two waves superpose destructively means crust of one wave fall on the trough of the another wave

{eq}\begin{align} y_{min} = y_1 - y_2 \end{align} {/eq}

{eq}\begin{align} y_{min} = 0.30 \ \rm m - 0.20 \ \rm m \end{align} {/eq}

{eq}\begin{align} \color{blue}{\boxed{ y_{min} = 0.10 \ \rm m}} \end{align} {/eq}


Learn more about this topic:

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The Resultant Amplitude of Two Superposed Waves

from MEGA Physics: Practice & Study Guide

Chapter 15 / Lesson 10
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