Question

A wave travelling on a string at a speed of 10 m s−1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? (b) If the displacement of a particle of 1⋅5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?

Answer 1

Displacement is 1.5 mm

Explanation:

Given,

Wave speed (v) = 10 $ms^-^1$

Time period (T) = $20\ ms = 20 \times 10^-^3 = 2 \times 10^-^2\ s$

a) Wavelength of the wave:

$\lambda = \nu t = 10 \times 2 \times 10^-^2$

=  0.02 m = 20 cm

(b) Displacement of the particle at a certain instant:

y = $asin(\omega t - kx)$

1.5 = $asin(\omega t - kx)$

Phase difference of the particle at a distance x = 10 cm:

$\phi = \frac {2\pix}{\lambda} = 2\pi \times \frac {10}{20} = \pi$

The displacement is given by

$y^o = asin(\omega t - kx +\pi)$

      = $asin(\omega t - kx)$ = 1.5 mm

Hence, Displacement = 1.5 mm