# Ratio of Resultant Wave to Common Amplitude: Pi/2 Rad Out of Phase

• bearhug
In summary, when two identical traveling waves are moving in the same direction and are out of phase by Pi/2 rad, the ratio of the amplitude of the resultant wave to the common amplitude of the waves can be found by adding the two sine waves and calculating the peak amplitude. The resulting ratio will be between 2:1 and 0, depending on the phase difference of the waves.
bearhug
Two identical traveling waves, moving in the same direction, are out of phase by Pi/2 rad.
(a) What is the ratio of the amplitude of the resultant wave to that of the common amplitude of the waves

I'm having trouble with this problem because I feel like I'm not given enough information, although I know that's not really the case. Does anyone have any recommendations as to where I can look up some information that can help me with this problem?

Can you write the equation for each of the traveling waves? Or even just add two sine waves that are out of phase by pi/2 -- what is the max amplitude?

I thought I was suppose to add the two amplitudes to get the resultant amplitude but I wasn't sure if that was if they were right on top of each other. Doing this would make the ration 2:1 but I don't think that's right.

It's only 2:1 if they are in phase. If they are 180 degrees out of phase, you get zero when you add them, right? And if they are 90 degrees off, you get some value in between 2:1 and 0. How can you figure out the peak amplitude of the addition?

## What is the ratio of the resultant wave to the common amplitude when the phase difference is pi/2 radians?

The ratio of the resultant wave to the common amplitude when the phase difference is pi/2 radians is 1:1. This means that the amplitude of the resultant wave is equal to the amplitude of the common wave.

## How does a phase difference of pi/2 radians affect the resultant wave?

A phase difference of pi/2 radians causes the resultant wave to be out of phase, meaning that the peaks and troughs of the waves do not line up. This results in a wave with a smaller amplitude than the common wave.

## Is a phase difference of pi/2 radians always present in waves?

No, a phase difference of pi/2 radians is not always present in waves. It only occurs when two waves with the same amplitude and frequency are combined at a 90 degree angle.

## What is the significance of a phase difference of pi/2 radians in wave interference?

A phase difference of pi/2 radians in wave interference results in destructive interference, where the waves cancel each other out and the resultant wave has a smaller amplitude. This phenomenon is commonly observed in sound waves and can be used to create noise-cancelling technology.

## How does the ratio of the resultant wave to the common amplitude change with different phase differences?

The ratio of the resultant wave to the common amplitude changes depending on the phase difference between the two waves. When the phase difference is 0 or a multiple of 2pi, the ratio is 2:1, meaning the amplitude of the resultant wave is twice the amplitude of the common wave. As the phase difference increases, the ratio decreases until it reaches 0 when the phase difference is pi or an odd multiple of pi.

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