#### A wave on a string meets with another wave producing a node at . Then the equation of the unknown wave is : Option 1) Option 2) Option 3) Option 4)

As we learnt in

Property of stationary waves -

1)    Disturbance do not move in any direction.

2)    All particles except nodes perform S.H.M.

3)    During the formation of a stationary wave the medium is broken into equally spaced loops

4)    Amplitude of the particle is different at different point

-

:    Consider option (a)

Stationary wave :

$Y=a\sin \left ( \omega t+kx \right )+a\sin \left ( \omega t-kx \right )$

when $x=0,$    $Y$ is not zero. The option is not acceptable.

Consider option (b)

Stationary wave :

$Y= a\sin \left ( \omega t-kx \right )-a\sin \left ( \omega t+kx \right )$

$At x= 0,Y= a\sin \omega t -a\sin \omega t= 0$

This option holds good

Option (c) gives$Y= 2a\sin\left ( \omega t -kx \right )$

At $x=0,Y\neq 0$

Option (d) gives Y = 0

Hence only option (b) holds good

Correct option is 2.

Option 1)

This is an incorrect option.

Option 2)

This is the correct option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.