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A transverse wave on a string has displacement y(x,t) = e^(-(ax² + bt² + 2abxt)). This corresponds to a:

1. wave travelling in the negative x-direction with speed √(b/a)
2. standing wave with frequency √b
3. standing wave with frequency 1/√b
4. wave travelling in the positive x-direction with speed √(a/b)

Correct answer: wave travelling in the negative x-direction with speed √(b/a)

Solution

The given displacement function represents a wave that has a specific form indicating it travels in the negative x-direction, as evidenced by the presence of the term involving both x and t in the exponent. The speed of the wave can be derived from the coefficients in the exponent, leading to the conclusion that it travels with speed √(b/a).

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