The transverse displacement $y(x, t)$ of a wave on a string is given by $y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.$ This represents $a:$
wave moving in $-x$ direction with speed $\sqrt {{b \over a}} $
standing wave of frequency $\sqrt b $
standing wave of frequency ${1 \over {\sqrt b }}$
wave moving in $+x$ direction speed $\sqrt {{a \over b}} $
Solution
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