Question

A wave is represented by the equation $y=\left[Asin\right(10x+15t+\frac{1}{3}\left)\right]$ where $x$ is in meters and $t$ is in seconds. The expression represents

• A. A wave travelling in positive x-direction with a velocity $1.5$ m/s.
  
• B. A wave travelling in negative x-direction with a velocity $1.5$ m/s
• C. A wave travelling in the negative x-direction having a wavelength $2$ m
• D. A wave travelling in positive x-direction having a wavelength $2$ m.

Answer 1

The correct option is B A wave travelling in negative x-direction with a velocity $1.5$ m/s

Wave equation is given as:

$y=A\sin (10x+15t+\frac{1}{3})$

If the time increases, $x$ must decrease to make that happen. That makes the location of the section of wave in consideration, the wave move in negative direction.

Hence, in this wave is travelling in negative $x-$direction.

Now, velocity of wave is,

$v=\frac{\omega }{k}=\frac{15}{10}$ (Here, $\omega =15$ and $k=10$)

$\Rightarrow v=1.5\frac{m}{s}$

Hence, option $B$ is correct