Question

A transverse harmonic wave on a string is described by
$y(x,t)=5\sin (10t+0.09x+\pi /3)$ where $x$,$y$ are in $cm$ and $t$ in $s$. The positive direction of $x$ is from left to right. The nature of the wave is

• A. standing
• B. stationary
• C. travelling
• D. none of these.

Answer 1

Answer: (C)

Equation of given harmonic wave is
$y(x,t)=5\sin \left(10t+0.09x+\frac{\pi }{3}\right)$ ....(i)
The standard equation for the travelling wave is
$y(x,t)=Asin\frac{2\pi }{\lambda }(\upsilon t-x+\varphi )$ or $y(x,t)=A\sin \left(\frac{2\pi t}{T}-\frac{2\pi x}{\lambda }+\varphi \right)$ .....(ii)
Comparison of (i) and (ii) shows that equation (i) represents the travelling waves .