Question

A wave is represented by the equation $y=A\sin (10\pi x+15\pi t+\pi /3)$
where $x$ is in metres and $t$ is in seconds. The expression represents :
(1) a wave travelling in the positive $x$-direction with a velocity $1.5m/s$
(2) a wave travelling in the negative $x$-direction with a velocity $1.5m/s$
(3) a wave travelling in the negative $x$-direction with a wavelength $0.2m$
(4) a wave travelling in the positive $x$-direction with a wavelength $0.2m$

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 are correct
• D. 1, 2 and 3 are correct

Answer 1

Answer: (B)

From the equation of wave $\omega =15\pi ,k=10\pi$
Speed of wave, $v=\frac{\omega }{k}=\frac{15\pi }{10\pi }=1.5m/s$
Wavelength of wave, $\lambda =\frac{2\pi }{k}-=\frac{2\pi }{10\pi }=0.2m$
In the equation $10\pi x$ and $15\pi t$ have the same sign.
Therefore, wave is travelling in negative $x$ direction.