Waves

JEE Main level, single correct, medium

40 of 142

Question 40 of 142

A travelling harmonic wave is represented by the equation y(x,t)=10−3sin⁡(50t+2x),y\left(x,t\right)={10}^{-3}\sin \left(50t+2x\right)\text{,} where xx and yy are in meter and tt is in seconds. Which of the following is a correct statement about the wave?

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Answer: (C) The wave is propagating along the negative xx -axis with speed 25ms−125m{s}^{-1}

Given wave equation, y(x,t)=10−3sin⁡(50t+2x)y\left(x,t\right)={10}^{-3}\sin \left(50t+2x\right)
This equation is similar to the equation of wave travelling along the negative xx-axis which is given by
y(x,t)=Asin⁡(ωt+kx)y\left(x,t\right)=A\sin \left(\omega t+kx\right)
After comparing, Angular frequency ω=50s−1\omega =50{s}^{-1}
Wave number k=2m−1k=2{m}^{-1}
The wave velocity, v=ωk=502=25ms−1v=\dfrac{\omega }{k}=\dfrac{50}{2}=25m{s}^{-1}

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