Question

if two waves with equal amplitude and wavelengths travel through a medium in such a way yhat a particular particle of the medium is at the crest of one wave and it the trough of the other wave at the same time, what will happen to that particle

Answer 1

The problem points two key reference information. Equal wavelength and amplitude. The particle positioned at the ends of the two waves' trough and crest respectively will remain stationary in position at point where the waves meet. This is due to the parallel forces experienced by the particle having mentioned that the both waves have same Amplitude and wavelength. The ends of both wave will not change since with equal wavelength, displacement of each wave would be same.

Answer 2

The particle will remain stationary due to interference.

Step-by-step explanation:

Given

2 waves of equal amplitude (A) and wavelength (λ)

At a given instance, one wave is at the crest which is the highest point while the other is at trough which is the lowest point at the same instance.

For the fact that these two waves have the same (equal) amplitude, the two waves will cancel one another at that particle if we superposed the two waves

..To find the resultant displacement of the 'effective' wave, we may superpose the two waves. Since their amplitudes are equal, we realize that at that particle, the two waves cancel each other out.

This is so because the principle of superposition states that, the resultant displacement at that point is equal to the sum of the displacements due to each individual wave, when two or more waves of the same type cross at some point.

To prove this, we have

Displacement = Wavelength 1 + Wavelength 2

Wavelength 1 = λ

Wavelength 2 = -λ (it is represented with negative because of the position of the two wavelength at any given instance)

Displacement = λ + (- λ)

Displacement = λ - λ

Displacement = 0

This proves that the particle will remain stationary.

This phenomenon is termed 'destructive interference.'