Phase Shift and Wave Addition

Classical Mechanics Level 2

Two sine waves of equal velocities v v , equal frequencies ω \omega , and equal amplitudes A A at a relative phase shift of π / 3 \pi/3 are added together. What is the amplitude of the result?

A 3 A\sqrt{3} A A 2 A 2A A / 2 A/2

Matt DeCross by Matt DeCross , 27, USA

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2 solutions

Xiangchen Kong
Mar 10, 2016

Let

Wave 1=A sinX

Wave 2=A sin(x+π/3)=Asin x/2 +A√3 cos x/2

Resultant Wave =W1+W2 =3 A sin x / 2+√3A cos x / 2=A(3 sin x / 2+√3 cos x/ 2)

For the resultant should be the format of RA sin(x+a)

R=√(a^2+b^2)=√(9/4+3/4)=√3

3 Helpful 0 Interesting 0 Brilliant 0 Confused

I think it would be better if you changed the wording to, "What would the amplitude of resultant wave?" and drop the maximum.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Updated, thanks for the redundant wording catch.

Matt DeCross - 5 years, 3 months ago

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