Question

A transverse wave is described by the equation

y = y₀ sin2π(ft - x/ λ)

The maximum particles velocity is equal to four times the wave velocity if

1. λ = πy₀/4
2. λ = πy₀/2
3. λ = πy₀
4. λ = 2πy₀

Answer 1

Correct Answer - Option 2 : λ = πy₀/2

\(\begin{array}{l} v\; = \;\frac{{dy}}{{dt}}\; = \;{y_0}2\pi f\cos 2\pi (ft - \frac{x}{{{\rm{\lambda \;}}}})\\ {v_{max}}\; = \;{y_0}2\pi f \end{array}\)

Wave velocity: \(v\; = \;f\lambda\)

Given: \({v_{max}}\; = \;4v \Rightarrow {y_0}2\pi f\; = \;4f\lambda \Rightarrow \lambda \; = \;\frac{{{y_0}\pi }}{2}\)