1. AP Physics Section 11-7 to 11-9 Wave Properties
A wave is a disturbance that carries energy through matter and space.
Waves can be caused by vibrations in a material (called the medium). This type of wave is a mechanical wave. Examples of media in which these waves propagate include water, air, rock, metal, ropes, etc.
Electromagnetic waves do not need a medium. They can travel through a vacuum.

2. The motion of the spring over time
Vibrations and waves
Waves are related to vibrations, including the Simple Harmonic Motion we saw in a moving spring:
The motion of the spring over time
creates a sinusoidal (sine) wave.

3. Types of mechanical waves
There are three types of mechanical wave:
Transverse — the material moves perpendicular to the wave motion.
Longitudinal — the material moves back and forth parallel to the wave motion.
Surface waves — the particles move both perpendicular and parallel to the wave motion.

4. Transverse waves
Wave direction
The animation shows a one-dimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.

5. Longitudinal waves
The animation shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Watch a red particle and its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

6. Surface waves
Particles in water waves move in circles. How does the radius change with depth?
Raleigh waves are present in earthquakes. How do the particles move here? Earthquakes also have surface waves called Love waves.

7. Love waves are named for
A.E.H. Love,
Professor of Natural Philosophy at Oxford U.
Raleigh waves
are named for
John W. Strutt,
Baron Raleigh.

8. Wave characteristics
Wave speed (v) — the displacement of the peak or compression of a wave in a certain amount of time. Measured in meters/second.
Amplitude (A) — the maximum displacement of a particle in the medium from its equilibrium position.
Wavelength (λ) — the distance between waves, peak to peak or compression to compression.

9. transverse wave A λ
A = amplitude
λ = wavelength

10. All in different phases
Individual particles in a wave are in phase if they have the same displacement from equilibrium and the same velocity. They are whole wavelengths apart. a b c d
Particles a, b, and c are in phase with each other. Particle d is 180° out of phase with a, b, and c.
Waves as a whole can be in or out of phase:
All in phase
All in different phases

11. Period (T) — the time in seconds for one wavelength of a wave to pass a given point. This is the time between successive crests (peaks) or compressions.
Frequency (ƒ) — the number of waves that pass in one second. Many physics texts use nu: ν.
Since period is seconds per wave, and frequency is waves per second, they are reciprocal values: 1
ƒ = T
The product of frequency and wavelength is the wave speed:
v = ƒ λ

12. Speed of a wave on a cord or string
The speed of a wave depends on the properties of the medium through which it travels. For a string or cord, the speed primarily depends on the tension in the string, FT, and the linear density: the mass per unit length, m/L. FT FT
v = =
m/L ρℓ
linear density
A certain guitar has a 25.0” string length. The linear density of one of the strings is 0.19 g/cm. The tension is 74 newtons. The 4th harmonic has two full waves on the string. What is the speed and frequency of the 4th?
v = ƒ λ
v =
62 m/s
25” =
0.635 m
λ =
0.318 m v λ
62 m/s
ƒ = = =
196 Hz ρℓ
= 0.19 g/cm =
0.019 kg/m
0.318 m

13. Wave Energy P E/t E W m2 Units: I = = = A A A t I ∝ A2 A = E = ½kA2
The particles in a medium undergo simple harmonic motion. Therefore, their energy is given by:
E = ½kA2
So, E ∝ A2. Wave energy is proportional to the square of the wave amplitude.
Intensity, I, is defined as the wave power per unit area, or the wave energy flowing through an area per unit time. P
E/t E W m2
Units:
I = = = A A
A t
Since the energy is proportional to A2, so is the intensity:
I ∝ A2
For a wave traveling outward from a point, the shape is spherical. The surface area of any sphere is:
A =
4πr2

14. P P I = = A 1 I2 r12 I ∝ = r2 I1 1 A ∝ r A2 r1 = A1
For a spherically propagating wave, the intensity is therefore: P P
I = = A
4πr2
Since the power is generated at the source, the intensity decreases with the inverse square of distance: 1 I2
r12
I ∝ = r2 I1
r22 1
Since I ∝ A2, we can conclude that:
A ∝ r
The amplitude decreases proportionally with increasing distance. A2 r1 = A1 r2