Question

A sinusoidal transverse wave traveling in the positive direction of an x-axis has
amplitude of 2.0cm, a wavelength of 10c and a frequency of 400Hz. If the wave equation is of the form

Answer 1

Assume that

A sinusoidal transverse wave traveling in the positive direction of an x-axis has

amplitude of 2.0cm, a wavelength of 10 cm and a frequency of 400 Hz. If the wave equation is of the form

$\xi=A\sin\omega (t-\frac{x}{v})$

find (1) the velocity of propagation of waves and (2) the maximum velocity of the particles of the medium.

Solution

(1)

$v=\lambda\nu=0.1\cdot 400=40$ $m/s$

(2)

$\frac{d\xi}{dt}=A\omega\cos(t-\frac{x}{v})$

$(\frac{d\xi}{dt})_{max}=A\omega=A\cdot2\pi\nu=0.02\cdot2\cdot3.14\cdot400=50.24$ $m/s$