Question

A transverse wave on a string is described by the wave function y(x, t) = 0.338 sin(1.15x + 86.0t) where x and y are in meters and t is in seconds. Consider the element of the string at x = 0. (a) What is the time interval between the first two instants when this element has a position of y

Answer 1

0.073 s

Explanation:

The equation of a progressive wave is given by:

y = Asin(kx + ωt)

where;

A is the amplitude of the wave in meters

y(x,t) is the displacement in meters

k = 2π/λ is the propagation constant

ω = 2π/T is the angular frequency in radian per seconds

T is the period ⇒ The time taken to complete one oscillation.

The equation now becomes;

y = Asin((2πx)/λ ± 2πt/T)

Comparing the given y(x, t) = 0.338 sin(1.15x + 86.0t) with the general equation;

2πt/T = 86.0t

T = 2π/86

T = 0.073 s