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The transverse displacement

Question:

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^{2}+b b^{2}+2 \sqrt{a b x}\right)}$. This represents a :-

 

  1. standing wave of frequency $\sqrt{b}$

  2. standing wave of frequency $\frac{1}{\sqrt{b}}$

  3. wave moving in $+x$ directionwith speed $\sqrt{\frac{a}{b}}$

  4. wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$

Correct Option: , 4

Solution:

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