Question

A transverse harmonic wave on a string is described by $y (x, t) = 5 \sin (10 t + 0.09 x + \pi/3)$ 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)

travelling

Answer 2

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