1. Tardigrade
  2. Question
  3. Physics
  4. A transverse harmonic wave on a string is described by y (x, t) = 5 sin (10 t + 0.09 x + π/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

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Q. 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

Oscillations

Solution:

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 .