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 $1.5 \,m / s$
(2) a wave travelling in the negative $x$-direction with a velocity $1.5 \,m / s$
(3) a wave travelling in the negative $x$-direction with a wavelength $0.2 \,m$
(4) a wave travelling in the positive $x$-direction with a wavelength $0.2 \,m$

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