91Ó°ÊÓ

The height of the rectangular peak of the wave 1 is$h=4\mathrm{unit}$

The width of the rectangular peak of the wave 1 is$d$

The depth of the rectangular peak of the wave 1 is$d=2unit$

Use the concept of standing waves. Apply the superposition principle for interference of the waves.

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

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.

a)

The deepest valley :

The wave (1) has depth and wave (4) has depth. When they interfere with each other, then their resultant has the deepest valley as according to the superposition principle.

Therefore, wave (1) can interfere with wave (4) that gives the deepest valley than other waves.

Hence, the left-going wave (4) will give interference for the deepest valley.

b)

A flat line:

When wave (1) interferes with wave (4), according to the superposition principle, they cancel each other. Hence, their resultant as a flat line is produced.

Hence, the left-going wave (4) will give interference for a flat line.

c)

A flat peak $2d$wide:

According to the superposition principle, when wave (1) interferes with wave (3), then their resultant has a level peak $2d$wide.

Hence, the left-going wave (3) will give interference for a flat peak$2d$wide.

Therefore, the deepest valley, a flat line, and a level peak $2d$wide can be found by using the superposition principle.