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  • The transverse displacement y(x,t) of a wave on a string is given by <img alt="y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex

The transverse displacement y(x,t) of a wave on a string is given by

y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}

This wave represents a-

Option: 1

Wave moving in -x direction with speed \sqrt{\frac{b}{a}}


Option: 2

Standing wave of frequency \sqrt{b}


Option: 3

Standing wave of frequency \frac{1}{\sqrt{b}}


Option: 4

Wave moving in +x direction with speed \sqrt{\frac{a}{b}}


Answers (1)

best_answer

\begin{aligned} y(x, t) & =e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)} \\ & =e^{-(\sqrt{a} x+\sqrt{b} t)^2} \end{aligned}

 

It is a function of type, y=f(wt+kx)

? y (x,t) represents wave travelling along -x direction.

\text { speed of wave }=\frac{\omega}{k}=\frac{\sqrt{b}}{\sqrt{a}}=\sqrt{\frac{b}{a}}

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Anam Khan

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