Question

What will be the amplitude of the resultant wave when two waves of same amplitude A, but with an initial phase difference of 30 degrees superimpose on each other?​

Answer 1

The equation of the two superimposing waves can be give by

y

1

=a

1

sin(ωt) and y

2

=a

2

sin(ωt+π/2)=a

2

cos(ωt).

So, the equation of the resultant wave is y=y

1

+y

2

=a

1

sin(ωt)+a

2

cos(ωt).

Assuming a

1

=acos(ϕ) and a

2

=asin(ϕ), we get

y=asin(ωt+ϕ).

Here a

1

2

+a

2

2

=a

2

(sin

2

(ϕ)+cos

2

(ϕ))=a

2

⇒a=

a

1

2

+a

2

2

.