Question

A particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.

Answer 1

Time taken to reach from the mean position to the extreme position, $\frac{T}{4}$ = 5 ms
Time period (T) of the wave:
$$\begin{gathered} T=4\times 5\mathrm{ms} \\ =20\times {10}^{-3}=2\times {10}^{-2}\mathrm{s} \end{gathered}$$
Wavelength (λ) = $2\times \mathrm{Distance}\mathrm{between}\mathrm{two}\mathrm{mean}\mathrm{positions}$
$=2\times 2\mathrm{cm}=4\mathrm{cm}$
$$\begin{gathered} \mathrm{Frequency},f=\frac{1}{\mathrm{T}} \\ =\frac{1}{\left(2\times {10}^{-2}\right)} \\ =50\mathrm{Hz} \\ \mathrm{Wave}\mathrm{speed},v=\lambda f \\ =4\times {10}^{-2}\times 50 \\ =200\times {10}^{-2} \\ =2\mathrm{m}/\mathrm{s} \end{gathered}$$