TS EAMCET · Physics · Waves and Sound

Two harmonic travelling waves are described by the equations $y_{1} = a \sin (k x - ω t)$ and $y_{2} = a \sin (- k x + ω t + ϕ)$ The amplitude of the superposed wave is

A $2 a \cos \frac{ϕ}{2}$
B $2 a \sin ϕ$
C $2 a \cos ϕ$
D $2 a \sin \frac{ϕ}{2}$

Verified Solution

Answer & Solution

Correct Answer

(D) $2 a \sin \frac{ϕ}{2}$

Step-by-step Solution

Detailed explanation

y1=asinkx-ωt ...1 y2=asin-kx+ωt+ϕ ...2 On adding 1 and 2, y1+y2=2asinkx-ωt+-kx+ωt+ϕ2 coskx-ωt+kx-ωt-ϕ2…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two harmonic travelling waves are described by the equations y1=asinkx-ωt and y2=asin-kx+ωt+ϕ The amplitude of the superposed wave is

Step-by-step Solution

Two harmonic travelling waves are described by the equations $y_{1} = a \sin (k x - ω t)$ and $y_{2} = a \sin (- k x + ω t + ϕ)$ The amplitude of the superposed wave is