Transverse Wave Interference

[Oijl]

Homework Statement

Having two identical waves, knowing how much they're out of phase with each other, how can I know the amplitude of the resulting wave (as a factor of the original amplitude)?

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Write down two wavw equations, say
A1 = Ao(sinwt + phy1) and A2 = Aosin(wt + phy2)
Add them to find the amplitude of the resultant wave.

 

[nlightner]

There are several ways to determine the amplitude of the resulting wave in a situation of transverse wave interference. One method is to use the principle of superposition, which states that when two waves overlap, the resulting displacement of the medium is equal to the sum of the individual displacements. In this case, if the two waves are identical and out of phase by a certain amount, the resulting wave will have an amplitude equal to the sum of the individual amplitudes. This can be calculated using the formula A = A1 + A2, where A is the amplitude of the resulting wave and A1 and A2 are the amplitudes of the individual waves.

Another method is to use trigonometric functions to determine the amplitude of the resulting wave. If the two waves are sinusoidal and out of phase by a certain amount, the resulting wave can be represented by a trigonometric function, such as the cosine or sine function. The amplitude of this function can be calculated using the formula A = A0 * cos(Δφ), where A0 is the original amplitude of the waves and Δφ is the phase difference between the waves.

It is important to note that the amplitude of the resulting wave will depend on the specific phase difference between the two waves. For example, if the two waves are completely in phase (Δφ = 0), the resulting wave will have an amplitude twice that of the individual waves. On the other hand, if the two waves are completely out of phase (Δφ = π), the resulting wave will have an amplitude of zero.

In summary, the amplitude of the resulting wave in a situation of transverse wave interference can be determined by using the principle of superposition or by using trigonometric functions, and will depend on the specific phase difference between the waves.