The transverse displacement \( y(x, t) \) of a wave on a string is given by \( y(x,t) = e^{-(x^2 + t^2)} \sin(kx - \omega t) \). This represents a:
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For a wave equation of the form \( y(x,t) = e^{-(x^2 + t^2)} \sin(kx - \omega t) \), the wave moves in the \( -x \) direction and its speed is \( \sqrt{\frac{b}{a}} \).