Physics

Physics

Problem

A transverse wave is described by the equation y=y0sin⁡2π(ft−xλ)y = y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right). The maximum particle velocity is equal to four times the wave velocity if a. λ=πy04\lambda = \pi \frac{y_0}{4} b. λ=πy02\lambda = \pi \frac{y_0}{2} c. λ=πy0\lambda = \pi y_0 d. λ=2πy0\lambda = 2\pi y_0
Intuitive explanation

The key is recognizing that particle velocity (how fast a point on the string moves up and down) is fundamentally different from wave velocity (how fast the wave pattern travels). Take the time derivative of the wave equation to find maximum particle velocity, then set up the ratio condition. The relationship between frequency, wavelength, and wave speed will be your bridge to finding the constraint on the wave parameters.

Intuitive explanation

The key is recognizing that particle velocity (how fast a point on the string moves up and down) is fundamentally different from wave velocity (how fast the wave pattern travels). Take the time derivative of the wave equation to find maximum particle velocity, then set up the ratio condition. The relationship between frequency, wavelength, and wave speed will be your bridge to finding the constraint on the wave parameters.

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