Question

To understand the standard formula for a sinusoidal traveling wave. One formula for a wave with a y displacement (e.g., of a string) traveling in the x direction is y(x,t)=Asin(kx−ωt).
All the questions in this problem refer to this formula and tothe wave it describes.a) Which are independent variables?b) Which are parameters that determine the characteristics ofthe wave?c) What is the phase phi(x,t) of the wave?d) What is the wavelength lambda of the wave?e) What is the period Tof this wave?f) What is the speed of propagation v of this wave?

Answer 1

Explanation:

The displacement of the sinusoidal wave traveling in the x direction is given by;

                                          y(x,t)=Asin(kx−ωt)

Where

A is the amplitude of wave  in meters

k is the propagation constant of the wave given by k = 2π/λ

ω $=\frac{2\pi }{T}$ is the angular frequency in radian per seconds

T is the period in seconds $T = \frac{2\pi }{w}$

(a) The independent variables are x and t

(b) Parameters that determine the characteristics of the wave are amplitude A, propagation constant k and angular frequency ω

(c) The phase phi(x,t) of the wave is (kx−ωt)

(d) The wavelength λ of the wave λ = 2π/k

(e) The period T of the wave is $T =\frac{2\pi }{w}$

(f)  The speed of propagation v of the wave;

                         wave velocity v = fλ

                                   v = (ω/2π) × (2π/k)

                                  $v =\frac{w}{k}$

    The speed of propagation v of the wave is $v =\frac{w}{k}$