Two waves y1=a sin (ω t-k x) and y2=a cos (ω t-k x) superimpose at a point :

Question

Two waves y1=a sin (ω t-k x) and y2=a cos (ω t-k x) superimpose at a point : (A) The resultant amplitude is √2 a (B) If I is the intensity of each source then I max =2 I (C) The resultant wave leads y1 by a phase angle of (π/4) (D) Data insufficient to arrive at options(B) and (C)

Tardigrade Admin · Accepted Answer

As the two given waves have a phase difference π / 2 we can use the vector superposition principal for the wave amplitudes to find the resulting amplitude and obtain

Q. Two waves $y_{1} = a sin (ω t - k x)$ and $y_{2} = a cos (ω t - k x)$ superimpose at a point :

The resultant amplitude is $2 a$

If $I$ is the intensity of each source then $I_{m a x} = 2 I$

The resultant wave leads $y_{1}$ by a phase angle of $\frac{π}{4}$

Data insufficient to arrive at options(B) and (C)

As the two given waves have a phase difference $π /2$ we can use the vector superposition principal for the wave amplitudes to find the resulting amplitude and obtain

Q. Two waves y1​=asin(ωt−kx) and y2​=acos(ωt−kx) superimpose at a point :

The resultant amplitude is 2​a

If I is the intensity of each source then Imax​=2I

The resultant wave leads y1​ by a phase angle of 4π​