The wave function for a traveling wave on a taut string is (in si units) y (x, t) = 0.340 sin 15πt - 4πx + π 4 (a) what are the speed and direction of travel of the wave? g

Given the wave function

y (x, t) = 0.340 sin (15πt - 4πx + π/4)

Generally a wave function is of the form

y (x, t) = A•Sin (wt - kx + θ)

Where

A is amplitude

w is angular frequency

θ is the phase angle

k is the wave number.

Then, comparing this with given wave function

k = 4π, w = 15π and θ = π/4

Speed and direction?

The speed of a wave function can be determined using wave equation

v = fλ

w = 2πf

Then, f = w/2π = 15π/2π = 7.5Hz

Also k = 2π/λ

Then, λ = 2π/k = 2π/4π = 0.5 m

Then,

v = fλ = 7.5 * 0.5

v = 3.75m/s

Direction

Since the time and distance coefficient have opposite sign, for an increasing time interval, the translation will have to increase in the positive direction to nullify the change and maintain the phase. Hence, the wave is traveling in the positive x direction