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Fundamentals Of Physics
Found in: Page 1076

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Short Answer

Add the quantities y1=10sinωt, y2=15sin(ωt+30°)and y3=5sin(ωt-45°) using the phasor method

The sum of wave is 26.83sinωt+8.5°.

See the step by step solution

Step by Step Solution

Step 1: Identification of given data

The equation of first wave is y1=10sinωt

The equation of second wave is y2=15sinωt+30°

The equation of third wave is y3=5sinωt-45°

Step 2: Understanding the concept

The amplitude of the resultant wave is equal to the vector sum of the amplitude of each wave.

Step 3: Determination of vertical and horizontal component of resultant wave

The horizontal component of the resultant wave is given as:

yh=10cos0°+15cos30°+5cos-45°yh=10+13+3.54yh=26.54

The vertical component of the resultant wave is given as:

yv=10sin0°+15sin30°+5sin-45°yv=3.96

The resultant amplitude of waves is given as:

yr=yh2+yv2yr=26.542+3.962yr=26.83

The direction of the resultant wave is given as:

tanθ=yvyhtanθ=3.9626.54θ=8.5°

Step 4: Determination of sum of wave

The sum of the wave is given as:

y=yrsinωt+θ

Substitute all the values in equation.

y=26.83sinωt+8.5°

Therefore, the sum of wave is 26.83sinωt+8.5°.

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