Resultant equation of two identical out of phase waves

[Any Help]

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?

 

[anlon]

Yes, this is correct. You may want to use LaTeX in the future to make your work more legible, but good work.

 

[Any Help]

Yes, this is correct. You may want to use LaTeX in the future to make your work more legible, but good work.

What do you mean LateX? Is there another way to solve it?

 

[anlon]

$\LaTeX$ is a formatting system for writing equations and papers that look nice. For example, instead of writing:
Ym=2ym.cos(π/10.0) therefore Ym/ym=2 cos(π/10.0)=1.902
You can write $$Y_m = 2y_m \cos{\left(\frac{\pi}{10}\right)} \Rightarrow \frac{Y_m}{y_m} = 2 \cos{\left(\frac{\pi}{10}\right)} = 1.902$$This can also be written inline with other text: $Y_m = 2y_m \cos{\left(\frac{\pi}{10}\right)} \Rightarrow \frac{Y_m}{y_m} = 2 \cos{\left(\frac{\pi}{10}\right)} = 1.902$ which is often useful. In the bottom left corner of the reply box there is a link to the forum LaTeX guide, which tells you how to do this in the forum (wrap standalone equations in "$$" without quotes and wrap inline equations with "##" without quotes).

 

[Any Help]

Okay I'll try it next time. Thanks :)