A transverse sinusoidal wave of amplitude $A$, wavelength $\lambda$ and frequency $n$ is travelling on a…
A transverse sinusoidal wave of amplitude $A$, wavelength $\lambda$ and frequency $n$ is travelling on a stretched string. The maximum speed of particle is $(1/10)\text{th}$ the speed of propagation of the wave.
(a) $A = \frac{\lambda}{20\pi}$
(b) $A = \frac{\lambda}{10\pi}$
(c) $\lambda = 20\pi A$
(d) Both (a) and (c)
Solution
Maximum velocity,
$v_{\text{max}} = A\omega = \frac{v}{10} = \frac{10}{10} = 1\text{ ms}^{-1}$
$\Rightarrow A\omega = A \times 2\pi n = 1 \Rightarrow n = \frac{10^3}{2\pi} \quad (\because A = 10^{-3}\text{ m})$
Since, $v = n\lambda \Rightarrow \lambda = \frac{v}{n} = \frac{10}{10^3/2\pi} = 2\pi \times 10^{-2}\text{ m}$