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Waves

Question

A transverse wave is expressed as, $y = y_{o} \sin 2 πf t$ For what value of λ, maximum particle velocity equals to 4 times the wave velocity?

$y_{o} \frac{π}{2}$

$2 y_{o} π$

$y_{o} π$

$y_{o} \frac{π}{4}$

Solution

$y_{o} \frac{π}{2}$

Given equation is

$y = y_{o} \sin 2 πf t$

Where $A = y_{o}, k = \frac{2 π}{λ}$

According to the question,

v = 4 $v_{p}$

∴ Aω = $4 \frac{ω}{k}$

∴ $y_{o} ω = \frac{4 ω}{k}$

⇒ $y_{o} = \frac{4}{k}$

⇒ $y_{o} = \frac{4}{2 π} \times λ$

Therefore, wavelength $λ = \frac{π y_{o}}{2}$