Question

A sinusoidal wave propagates along a string. In figure (a) and (b) 'y' represents displacement of particle from the mean position. 'x' & 't' have usual meanings. Find :-

(a) y(in mm)↑

(b) y(in mm)↑

(a) wavelength, frequency and speed of the wave (b) maximum velocity and maximum acceleration of the particles

Answer 1

(a) Wavelength $\lambda = 4$ m, Frequency $f = \frac{1}{4}$ Hz, Speed $v = 1$ m/s. (b) Maximum velocity $v_{y,max} = \frac{3\pi}{2}$ mm/s, Maximum acceleration $a_{y,max} = \frac{3\pi^2}{4}$ mm/s$^2$.

Answer 2

The solution involves extracting amplitude, time period, and wavelength from the given displacement-time and displacement-position graphs. These values are then used to calculate frequency and wave speed. For particle velocity and acceleration, the relationship between displacement, amplitude, and angular frequency is used to find their maximum values.