### JEE Main 12 Jan 2019 Morning Question 16

##### Question: A travelling harmonic wave is represented by the equation $ y(x,t)={10^{-3}}\sin (50t+2x), $ where x and t are in meter and t is in seconds. Which of the following is a correct statement about the wave? [JEE Main Online Paper Held On 12-Jan-2019 Morning]

#### Options:

A) The wave is propagating along the positive x-axis with speed $ 25,m,{s^{-1}} $ .

B) The wave is propagating along the positive x-axis with speed $ 100,m,{s^{-1}} $ .

C) The wave is propagating along the negative x-axis with speed $ 25,m,{s^{-1}} $ .

D) The wave is propagating along the negative x-axis with speed $ 100,m,{s^{-1}} $ .

## Show Answer

#### Answer:

Correct Answer: C

#### Solution:

The given wave is $ y(x,t)={10^{-3}}\sin (50t+2x) $

Comparing with standard equation $ y(x,t)=a\sin (\omega t+\beta x) $

Velocity $ v=\frac{\omega }{\beta }=\frac{50}{2}=25m,{s^{-1}} $ In the given equation x is positive.

Therefore, the wave is travelling in the negative x-direction.