# Resultant equation of two identical out of phase waves

• Any Help
In summary: 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)=1.902You 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)} \
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?

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

anlon said:
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?

##\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).

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

## What is the resultant equation of two identical out of phase waves?

The resultant equation of two identical out of phase waves is the sum of the two individual wave equations. It takes into account the amplitude, frequency, and phase shift of both waves to determine the overall behavior of the resulting wave.

## How is the amplitude affected by two identical out of phase waves?

When two identical out of phase waves interfere, they cancel each other out and the resulting wave has an amplitude of zero. This is because the peaks of one wave align with the troughs of the other, resulting in destructive interference.

## What happens to the frequency of the resulting wave when two identical out of phase waves interfere?

The frequency of the resulting wave remains the same as the individual waves. This is because frequency is determined by the source of the wave, not by interference with other waves.

## Can two identical out of phase waves produce a standing wave?

No, two identical out of phase waves cannot produce a standing wave. This is because the waves cancel each other out and do not have any points of constructive interference to form the characteristic nodes and antinodes of a standing wave.

## How does the phase shift affect the resulting wave of two identical out of phase waves?

The phase shift of the resulting wave is determined by the phase shift of the individual waves. If both waves have the same phase shift, the resulting wave will have the same phase shift. If the phase shifts of the individual waves are different, the resulting wave will have a phase shift somewhere in between.

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