The transverse displacement \( y(x, t) \) of a wave on a string is given by \( y(x, t)=e^{\left(....

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The transverse displacement \( y(x, t) \) of a wave on a
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string is given by \( y(x, t)=e^{\left(a x^{2}+b t^{2}+2 \sqrt{a b} x t\right)} \)
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This represents a:
(1) Wave moving in \( -x \) direction with speed \( \sqrt{\frac{b}{a}} \)
(2) Standing wave of frequency \( \sqrt{b} \)
(3) Standing wave of frequency \( \frac{1}{\sqrt{b}} \)
(4) Wave moving in \( +x \) direction speed \( \sqrt{\frac{a}{b}} \)


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