Comprehension for Q. 52 and 53: One wave travelling along a stretched string is y 1 ( x , t ) = y m sin ( k x − ω t ) and another, shifted from the first, is y 2 ( x , t ) = y m sin ( k x − ω

Question

Comprehension for Q. 52 and 53: One wave travelling along a stretched string is $y_{1} (x, t) = y_{m} sin (k x - ω t)$ and another, shifted from the first, is $y_{2} (x, t) = y_{m} sin (k x - ω t + ϕ)$ . Both waves travel in the positive direction of the $x$ -axis with the same speed. The equation of the resultant wave is $y' (x, t)$ equal to:

Options:

Answer:

C

Solution:

The second wave is $y_{2} = y_{m} sin (k x - ω t + ϕ)$ . Then $y' = y_{1} + y_{2} = 2 y_{m} cos \frac{ϕ}{2} sin (k x - ω t + \frac{ϕ}{2})$ .

TestHub · Accepted Answer

The second wave is y 2 ​ = y m ​ sin ( k x − ω t + ϕ ) . Then y ′ = y 1 ​ + y 2 ​ = 2 y m ​ cos 2 ϕ ​ sin ( k x − ω t + 2 ϕ ​ ) .

Physics - Wave on String Question with Solution | TestHub

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