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Question

Two harmonic waves are represented in SI units by, y1 (x, t) = 0.2 sin (x 3.0t) and y2 (x, t) = 0.2 sin (x3.0t + ϕ). What is the expression for the sum y = y1 + y2 for ϕ =π2.


A

y = 8 sin (x - 3.0t)

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B

y = 0.28 sin (x - 3.0t+π4)

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C

y = 0.2 sin (x - 3.0t+π4)

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D

y = 0.28 cos (x - 3.0t+π4)

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Solution

The correct option is B

y = 0.28 sin (x - 3.0t+π4)


The two waves y1(x1t)=0.2sin(x3.0t)

y2(x1t)=0.2sin(x3.0t+ϕ)

Given,ϕ=π2

Drawing a phase diagram

Resultant amplitude A=(0.2)2+(0.2)2+2×0.2×0.2cos(π2)

A=2×0.2=0.28 m

The new phase θ=tan1(0.20.2)=π4

Sot the wave equation for y=y1+y2

y=0.28sin(x3.0t+π4)


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