Question 188: Waves

Question

A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ Then the equation of the unknown wave is

Accepted Answer

To form a node there should be superposition of this wave with the reflected wave. The reflected wave should travel in opposite direction with a phase change of $$\pi $$. The equation of the reflected wave will be
$$y = a\sin \left( {\omega t + kx + \pi } \right)$$
$$ \Rightarrow y =  - a\sin \left( {\omega t + kx} \right)$$

Answer

$$y = a\,\sin \,\left( {\omega t + kx} \right)$$

Answer

$$y =  - a\,\sin \,\left( {\omega t + kx} \right)$$

Answer

$$y = a\,\sin \,\left( {\omega t - kx} \right)$$

Answer

$$y =  - a\,\sin \,\left( {\omega t - kx} \right)$$

Waves

A wave $y=a \sin \left( {\omega t - kx} \right) on a string meets with another wave producing a node at x=0.$ Then the equation of the unknown wave is

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