Question

A standing wave is formed by the superposition of two travelling in opposite directions. The transverse displacement is given by
$y(x,t)=0.5sin\left(\frac{5\pi }{4}x\right)cos\left(200\pi t\right)$.
What is the speed of the travelling wave moving in the positive x direction?
(x and t are in meter and second, respectively.)

• A. $160m/s$
• B. $90m/s$
• C. $180m/s$
• D. $120m/s$

Answer 1

The correct option is A $160m/s$

The given equation is

$y(x,t)=0.5sin\left(\frac{5\pi }{4}x\right)cos\left(200\pi t\right)$

$y(x,t)=0.25\times 2sin\left(5\pi x/4\right)cos\left(200\pi t\right)$

$y(x,t)=0.25\left[sin\right(5\pi x/4+200\pi t)+sin(5\pi x/4-200\pi t\left)\right]$

From the above equation,

$\omega =200\pi$

$k=\frac{5\pi }{4}$

Velocity, $v=\frac{\omega }{k}$

$v=\frac{200\pi }{5\pi /4}=160m/s$

The correct option is A.