A mechanical wave is a disturbance that travels through a medium from one location to another, transporting energy. The traveling wave can be observed (as in the ocean) by the movement of the crest from one position in the medium to another.
The amplitude
y(x,t) of a sinusoidal wave varies with both distance (
x) and time (
t) travelled as shown in the relationship below where the wave is traveling in the forward direction.
| y(x,t) = Ycos | ( | 2π | t – | 2π | x + Φ | ) |
| T | λ |
The terms in t and x after the cos would be added (not subtracted) if the wave were travelling in the reverse direction.
At a particular time t (such as t
0), the terms in blue are constant, and there is a sinusoidal variation in space (with
x) for a wave with wavelength λ.
| y(x,t) = Ycos | ( | 2π | t – | 2π | x + Φ | ) |
| T | λ |
.Depite being cos(-x), the curve looks like cos(x) because cos(x) = cos(-x) three different times
The red, blue and green curves show the variation of
y(
x,
t) with
x at different times.
The phase (starting point) of the wave is different (due to
t being different), but the wavelength is the same.
At a particular distance
x, the terms in red are constant, and there is a sinusoidal variation in time(
t) with period
T.
| y(x,t) = Ycos | ( | 2π | t – | 2π | x + Φ | ) |
| T | λ |
three different distances
The purple, magenta and gold curves show the variation of
y(
x,t) with time
for three different values of
x. The phase (starting point) of the wave is different due to
x being different but the period
T is the same.