Eduprobe
Question:
The transverse displacement y(x,t) of a wave on a string is given by y(x,t) = e⁻(ax² + bt² + 2√abxt). This represents a:
standing wave of frequency √ab
wave moving in +x direction with speed √ab
wave moving in -x direction with speed √ab
standing wave of frequency 1/√ab
Solution:
Given that y = e⁻(ax² + 2√abxt + bt²) = e⁻(√ax + √bt)² = e⁻√a(x + √(b/a)t)²
The given displacement equation is of the form y = f(x + vt)
Thus, the wave moves in -x with a speed of v = √(b/a)