Question

A longitudinal wave is represented by $x =10 \sin 2 \pi\left( nt -\frac{ x }{\lambda}\right) cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

• A. $2 \pi$
• B. $5 \pi$
• C. $\pi$
• D. $\frac{5 \pi}{2}$

Answer 1

Answer: (B)

$V _{ P } \max =4 V _{\text {wave }}$
$\omega A =4\left(\frac{\omega}{ k }\right) $
$\Rightarrow A =\frac{4 \lambda}{2 \pi}$
$\lambda=\frac{2 \pi A }{4}$
$ \Rightarrow \frac{20 \pi}{4} $
$\Rightarrow 5 \pi$