11.3. Waves and Wave Properties

Oscillations produce waves

Consider a group of swings at a playground. Each one is an oscillator. If we tie them one to another with ropes, and then start to swing in the first one, the connecting ropes will cause the other swings to start oscillating as well.

You have created a travelling disturbance.

Waves

A wave is a disturbance that propagates from one location to another, carrying energy as it travels.

It is important to distinguish between the motion of the wave itself and the motion of the individual particles. A wave (PE and KE) can propagate long distances while the particles move only locally.

Wave Creation

A wave pulse can be created on a string by a quick up-and-down motion. Because the molecules in the

string are attached by bonds, the upward moving molecules on one end will pull the adjacent molecules upward, which in turn will pull the molecules next to them upward, etc., and the wave disturbance will propagate. The particles do not.

Simple harmonic motion will produce a sine wave.

Types of Waves

Transverse waves

The particles oscillate perpendicular to the direction of wave propagation

E.g. a wave that moves horizontally while the particles oscillate vertically around a fixed location.

Types of Waves

Longitudinal waves

The particles oscillate parallel to the direction of wave propagation

E.g. a wave that moves along the x-axis while the particles oscillate along the x-axis around a fixed location.

Sound waves are longitudinal waves

molecules in contact with it. These air pressure fluctuations (not the air molecules) propagate outward.

The ear drum detects sound in the same way.

A vibrating drum membrane causes alternate compressions and rarefactions of the density of air

Combination waves

Only longitudinal waves can propagate through a fluid of constant density, because any transverse

motion in such a fluid would not experience a restoring force.

However, if and where there is a density gradient

within a fluid, and at the interface between fluids of different density, transverse waves may

propagate.

Combination waves

Surface water waves are a

combination of transverse and

longitudinal waves.

So are waves

that travel through the

ground due to earthquakes.

Wave Properties

Wave Properties

Wave Properties

Wave Properties

Example 1

Types of Waves

Mechanical waves travel through matter---i.e. require matter for propagation. Sound waves and water waves are examples of mechanical waves.

Electromagnetic waves can travel through a vacuum. Radio waves and light waves are examples of electromagnetic waves. EM waves can travel through matter as well, e.g. glass.

Waves travel at different speeds in different materials

The speed of a wave is determined by the properties of the material, or medium, through which it travels. A medium can be a solid, liquid or gas.

In general, waves travel faster in a medium that is hard, and slower in a medium that is squishy (compressible). For example, sound waves travel at 343 m/s in air, 1400 m/s in water, and 5960 m/s in steel.

Speed of a longitudinal wave

Material

Steel

Aluminum

Marble

Concrete

Bone

Brick

Wood

Mercury

Water

Ethyl alcohol

Air (at STP)

Elastic Modulus of compressibility

Wave speeds also depend on various properties of the medium

Speed of a wave on a cord

Wave Reflection

An echo is an example of wave reflection. The sound wave “bounces” (reflects) off a solid object and travels back.

In general, waves reflect when they hit a barrier. The nature of the reflected wave depends on the type of barrier.

In the case of an echo, distance to the barrier also matters, since sound travels at 343 m/s.

Wave Reflection: Inverted

When a string is anchored firmly to a wall, an incoming upward wave pulse will exert an upward force on the wall. The wall will exert an equal and opposite force on the string. Therefore, on reflection, the wave is inverted.

Wave Reflection: Non-Inverted

When the far end of a string is free to move, an incoming wave pulse will move the ring upward and then back down---just like the motion that created the wave. Therefore, on reflection, the wave is not inverted. This is the case for a water wave.

Wave Reflection: Observations

Fixed-end reflection: Free-end reflection:

Time 1:

Time 2:

Partial Reflection: 1-D

If a light rope is tied to a heavy rope---i.e. there is a transition to a new medium---partial reflection will occur. The frequency of the transmitted wave will be

Partial Reflection: 1-D

Partial reflection also occurs for light waves.

Incoming light Reflected light

Transmitted light

Two-Dimensional Waves

For 2-D or 3-D waves, we can identify wave fronts, meaning all the points forming a wave crest. A line perpendicular to the front and in the direction of propagation is called a ray, (a). Wave fronts far from their source have such a large radius of curvature that they are approximately flat, and are called plane waves, (b).

Two-Dimensional Reflection

For the reflection of a 2-D plane waves, the angle of the reflected rays and wave fronts will equal the angle of the incident (incoming) rays and wave fronts.

Refraction

slower medium

Refraction Moving into a slower medium, the rays become more perpendicular to the interface. That is, the angle of refraction is less than

the angle of incidence.

Similarly, the ray of a wave going from a slower medium to a faster one would bend away from the perpendicular.

Refraction We can calculate the angle of refraction as follows:

Laser Demo showing reflection and refraction

Diffraction

When waves encounter an obstacle, there will be a “shadow region” behind the object.

However the waves will gradually bend around behind the object. This is called diffraction.

Diffraction

Diffraction

Diffraction

Waves Carry Energy

Wave Energy