Question

A transverse harmonic wave on a string is described by
y(x1
t) = 3.0 sin(36t + 0.018x)
find (i) amplitude of particle velocity. (ii) wave velocity.

Answer 1

A transverse harmonic wave on a string is described by y = 3.0 sin(36t + 0.018x)

on comparing this equation with standard equation of wave y = Asin(ωt + kx)

we get, amplitude, A = 3.0 cm

angular frequency, ω = 36 rad/s

wave number , k = 0.018 cm-¹

we know, wave velocity , v = ω/k

= 36/0.018

= 36000/18 = 2000 cm/s = 20 m/s

so, amplitude = 3cm

amplitude = 3cmwave velocity = 20 m/s