[western50]

how to decide In what direction is the wave traveling from the equation?

A transverse harmonic wave travels on a rope according to the following expression:

y(x,t) = 0.14sin(3x + 17.5t)

The mass density of the rope is μ = 0.135 kg/m. x and y are measured in meters and t in seconds.

+x direction
-x direction
+y direction
-y direction
+z direction
-z direction

[Unknown008]

EDIT: See below

[jcaron2]

Since time is always increasing, the argument of the sine is continually getting larger for a given value of x. That means that the wave will appear to be moving left (in the -x direction). This is analogous to the fact that the plot of f(x+a) is shifted a units to the left of the plot of f(x).

In general, the wave equation will have a sinusoidal function whose argument consists of a time component (with variable t) and a position component (with variable x in this case). The variable in the position component is the axis of travel (so in this case you automatically know that the direction of travel is along the x-axis). As for determining the sign of the propagation direction, if the signs of the time and position terms are the same, the wave will travel in the negative direction (left in this case). If the signs are different, the wave will travel in the positive direction.