Chapter 16: Waves - I (Summary)
What are the different types of waves?
Mechanical, Electromagnetic and Matter waves.
What is the difference between them?
What is the difference between a transverse wave and a
longitudinal wave?
What does the speed of a mechanical wave depend on?
Characteristics of the medium: tension and linear mass density.
How do you mathematically describe a wave?
f(x -/+ v t)
y(x,t) = ym sin(k x – w t + f)
y, x, t, f, A, k, w, T, v, transverse speed/ acceleration
What if the wave is moving to the left?
(average) Transmitted Power: P = ½ m v w2 ym2
Superposition of (linear) waves and interference:
y1(x,t) = ym sin(kx-wt) and y2 (x,t) = ym sin(kx-wt+f)
What happens when you add: y = y1 + y2 ?
y*(x,t) = 2 ym cos(f/2) sin(kx-wt+ f/2)
What if f = 0?
What if f = p?
Standing waves: two sinusoidal with the same amplitude,
frequency and wavelength but traveling in opposite
directions.
y1 = ym sin(kx-wt) and y2 = ym sin(kx+wt)
y = 2 ym sin(kx) cos(wt)
What is the difference between standing waves and traveling
waves?
Positions of nodes (N) and antinodes (A) in standing waves.
Is there any energy in the wave? Is there any “net” energy
transmission? How long does it take for a node position to
become an antinode? When is the (elastic) potential energy
the highest? When is kinetic energy the highest?
Hard and soft Reflections, and transmission
Standing waves in a string:
The string [of length L] is fixed (nodes) at both ends. Also,
we know that v = l f. The The string resonates [large,
sustainable amplitudes] at resonant frequencies.
ln = 2L/n
(n: integer)
fn = v/ln = nv/2L = (n/2L) (F/m)1/2
f n = n f1
(harmonic series)
n = 1: first harmonic [fundamental frequency]
n = 2: second harmonic
general n : nth harmonic