16.2 Mathematics of Waves

What is a pulse?

A single disturbance that moves through a medium with constant shape and amplitude.

How far does a pulse travel?

Δ𝑥=𝑣Δ𝑡

What does a wave function describe?

The position of particles in the medium as a function of position and time.

General sinusoidal wave equation?

$$y(x,t)=Asin(kx-{ω}t+{ϕ})$$

What does each variable mean, A, k, ω, ϕ, x,t?

A = amplitude, k = wave number, ω = angular frequency, ϕ = phase shift, x,t = position and time.

How do you tell wave direction from equation?

For $kx-{ω}t$ → moves right (+x), and for $kx+{ω}t$ → moves left (−x)

How to find amplitude?

It’s the coefficient A in the equation.

Is wave speed the same as particle speed?

No — particles oscillate, wave moves forward.

What does the wave equation mean?

It relates how the wave curves in space to how it accelerates in time.

What is superposition?

Waves add together when they overlap.

Resulting wave formula?

$y = y_1 + y_2$.

Does interference change wave speed?

No, speed stays the same.