Question 498: Waves

Question

The equation of a simple harmonic wave is given by
y = 3 sin$${\pi  \over 2}$$(50t $$-$$ x), 
where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

Accepted Answer

$$y = 3\sin {\pi  \over 2}\left( {50t - x} \right)$$
$$y = 3\sin \left( {25\pi t - {\pi  \over 2}x} \right)$$ on comparing with the standard wave equation
$$y = a\sin \left( {\omega t - kx} \right)$$
Wave velocity $$v = {\omega  \over k} = {{25\pi } \over {\pi /2}} = 50\,m/\sec $$
The velocity of particle
$${v_p} = {{\partial y} \over {\partial t}} = 75\pi \cos \left( {25\pi t - {\pi  \over 2}x} \right)$$
$${v_{p_{\max}}} = 75\pi $$
then $${{{v_{{p_{\max }}}}} \over v} = {{75\pi } \over {50}} = {{3\pi } \over 2}$$

Answer

2$$\pi $$

Answer

$${3 \over 2}\pi $$

Answer

$$3\pi $$

Answer

$${2 \over 3}\pi $$

Waves

The equation of a simple harmonic wave is given by y = 3 sin${\pi \over 2}(50t -$ x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

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