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The transverse displacement y(x,t) of a wave on a string is given by y(x,t) = e^(−(ax² + bt² + 2√ab xt)). This represents a:

1. wave moving in −x direction with speed √(b/a)
2. standing wave of frequency √b
3. standing wave of frequency 1/√b
4. wave moving in +x direction speed √(a/b)

Correct answer: wave moving in −x direction with speed √(b/a)

Solution

The given equation represents a wave that is influenced by both space and time variables, indicating it is a traveling wave. The negative sign in the exponent associated with the term involving xt suggests that the wave is propagating in the negative x direction, and the speed of this wave can be derived from the coefficients of the equation, resulting in a speed of √(b/a).

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