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## Homework Statement

Two identical traveling waves, moving in the same direction, are out of phase by

*π*/5.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude

*ym*of the two combining waves? (Give the answer as the ratio of the total amplitude to the common amplitude.)

## Homework Equations

Let y=ym.sinx be the equation of a wave where x is a variable time dependent. and ym is the maximum amplitude.

Let y=ym.sin(x+

*π*/5.0) be the equation of a second identical wave but out of phase by

*π*/5.0

In trigonometric equations: sin(a)+sin(b)=2sin(0.5(a+b)).cos(0.5(a-b))

## The Attempt at a Solution

the resultant equation will be:

Y=ymsinx + ym.sin(x+

*π*/5.0)

Y=ym(sinx + sin(x+

*π*/5.0))

....but sinx + sin(x+

*π*/5.0)=2sin(0.5(x+x+

*π*/5.0)).cos(0.5(x-x-

*π*/5.0))

....=2sin(x+

*π*/10.0).cos(

*π*/10.0)

Y=ym(2sin(x+

*π*/10.0).cos(

*π*/10.0))

then Ym=2ym.cos(

*π*/10.0) therefore Ym/ym=2 cos(

*π*/10.0)=1.902

is that correct ? and is that the ratio they want?