question_answer

A wave \[y=a\sin \,(\omega t-kx)\] on a string meets with another wave producing a node at \[x=0\]. Then, the equation of the unknown wave is                                   [AIEEE 2002]

A)  \[y=a\sin \,(\omega \,t+kx)\]      

B)  \[y=-a\sin \,(\omega \,t+kx)\]

C)  \[y=a\sin \,(\omega \,t-kx)\]

D)  \[y=-a\sin \,(\omega \,t-kx)\]

Correct Answer: B

Solution :

[b] Equation of a wave

... (i)

Let equations of another wave may be

... (ii)

... (iii)

If Eq. (i) propagates with Eq. (ii), then we get the resultant wave

... (iv)

If Eq. (i) propagates with Eq. (iii), then we get

. (v)

After putting  in Eqs. (iv) and (v) respectively, we get

and

Hence, Eq. (iii) is a equation of unknown wave.