Question

A sinusoidal wave travelling in the same direction have amplitudes of 3 cm and 4 cm and difference in phase by `pi/2`. The resultant amplitude of the superimposed wave is ______.

पर्याय

• 7 cm 

• 5 cm 

• 2 cm

• 0.5 cm

Answer 1

A sinusoidal wave travelling in the same direction have amplitudes of 3 cm and 4 cm and difference in phase by `pi/2`. The resultant amplitude of the superimposed wave is 5 cm.

Explanation:

Given, 

a₁ = 3 cm

a₂ = 4cm

Φ = `pi/2` = 90°

The resultant amplitude of the superimposed wave is

R = `sqrt("a"_1^2+"a"_2^2+2"a"_1"a"_2cosphi)`

= `sqrt((3)^2+(4)^2+2xx3xx4xxcos90°)`

= `sqrt(9+16+24xx0)`

= `sqrt(9+16)`

= `sqrt25` cm

R = 5 cm