Question

If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and then somehow phase-shift one of them by 5.4wavelengths, what type of interference will occur on the string?

Short answer

The interference will be intermediate closer to fully destructive.

Step-by-step solution

The given data

1. The two waves have the same amplitude.
2. $\varphi =5.4\lambda$
   

Determining the concept

Use the concept of phase difference and their resulting interference types.

The phase difference is known as the cycle difference between two waves at the same point. Overlapping waves that have the same cycle are known as waves in phase, while waves with phase differences that do not overlap are known as out of phase waves.

Formulae are as follow:

$y\text{'}\left(x,t\right)=y_1\left(x,t\right)+y_2\left(x,t\right)$

Where, t is time , x-y axis.

Determining the type of interference that will occur on the string

The type of interference:

According to the superposition principle, if two sinusoidal waves of the same amplitude travel along the stretched string, they interfere and produce a resultant wave.

But here, the phase difference as 5.4 wavelength. It indicates that the peak of the shifted sine will be 0.4 wavelength ahead of the non-shifted sine.

According to the concept of phase difference and resulting interference types, at 0.5 wavelength, the phase difference is a fully destructive interference.

Hence, the interference for 0.4 wavelength is intermediate closer to fully destructive.

Therefore, the type of interference can be determined by using the concept of phase difference and resulting interference type.