Chapter 14: Waves

What’s disturbing you?

Wave Properties

Waves carry energy through matter. The matter can move with the wave, or at

right angles to it. Newton’s laws and conservation laws

govern the behavior of waves as well as particles.

All waves transmit energy. Some we see and some we cannot, like sound and light.

What are Waves? Rhythmic disturbances that carry energy

through matter or space are called waves.

Some waves require a medium to travel through. These are called Mechanical waves.

Water, air, ropes, and springs can “carry” energy through them.

Media can be solids, liquids, or gases. Some are good carriers and some not so good…

Two types of wavesThere are two different fundamental types of

waves: Transverse Waves- the energy moves at

right angles to the direction of the medium. Water, light, waves on a rope, electromagnetic waves,

most waves move this way

Longitudinal Waves- the energy moves parallel with the direction of the medium.

Sound & slinky compressions are the only examples of a longitudinal or compression wave. Most liquids & gases transmit energy this way.

Identifying Waves

Measuring WavesWe can describe waves in several aspects: Speed- Δd/Δt, speed depends on medium Amplitude- maximum displacement from

rest or equilibrium. Greater amplitude is caused by more work, thus more energy (not more speed)

For waves of the same speed, the rate at which energy is transferred is proportional to the square of the amplitude. Double amplitude transfers 4x as much energy/sec.

Measuring waves cont’d

Wavelength (λ)- low points are troughs, high points are crests, shortest distance b/t 2 identical points on a wave is one wavelength (m).

Period (T)- the time it takes for a wave to make one complete cycle (oscillation). (s)

Frequency (f)- the number of cycles per second (Hz).

fT

1

Tf

1

Wave Speed

Both period and frequency of a wave depend only on the wave source; not speed or medium.

Wavelength depends on both frequency and wave speed. Speed of a wave is wavelength divided by period, so

Wave speed is frequency times wavelength.

fv T

v

Example Problem

A sound wave produced by a clock chime is heard 515 m away, 1.5 s later.

a. What is the speed of sound of the

clock’s chime in air?

b. The sound wave has a frequency of

436 Hz. What is its period?

c. What is its wavelength?

Problem Solved

Given: d = 515m, t=1.5s, f=436 Hz

v = d / t, T = 1/f

a. v = 515m / 1.5s = 343m/s

b. T= 1/f = 1/436Hz, T=2.29x10-3s

c. λ = v / f = (343m/s) / (436Hz) = 0.787m

Sonic Boom

Sonic Boom Meets Sun Dog

Wave Behavior When a wave reaches a boundary, some of the

wave reflects back into the original medium, and some of the wave is transmitted into a new medium.

The amount of reflection or refraction depends on rigidity of the medium.

Waves at Boundaries Remember the speed of a wave through a

medium depends on the properties of the medium, not wave amplitude or frequency.

In air, temperature affects speed. In water, depth affects speed. In solids, rigidity affects speed. Waves striking boundaries may be

returned to their medium (reflected), or passed through to the next (transmitted).

Boundaries cont’d An incoming wave is called an INCIDENT

WAVE. If an incident wave strikes a barrier and is

transmitted, the pulse remains upward. If an incident wave strikes a barrier and is

reflected, the pulse returns to the original medium and can be inverted.

Reflected waves can lose amplitude and transfer energy to the barrier. The wave’s speed does not really decrease.

Superposition Unlike particles of matter, 2 or more waves

can exist in the same space at the same time.

The medium will be displaced an algebraic equivalent to the sum of the individual displacements.

This is called interference and can increase (Constructive) or decrease (Destructive) the amplitude of the new wave.

Wave Interference Interference can produce

points of zero displacement called nodes.

Points of maximum displacement are called antinodes.

Standing waves appear to stand still due to interference at just the right frequency.

Waves in two-dimensions Ray diagrams help model the movement

of waves in 2 dimensions. A line perpendicular to the barrier is the

“normal” The angle an incident ray makes with the

normal will be equal to the angle a reflected ray makes with the normal

This is the law of reflection and holds true for all types of waves.

Reflection and Refraction Waves that return to their

medium reflect from a surface following the law of reflection.

Waves that pass through to another medium refract or bend due to a change in speed in the new medium.

Diffraction

Waves may bend AROUND a barrier they encounter. Bending around the edges without changing media is called diffraction.

Diffraction also occurs when waves meet a small obstacle. They can bend around it and fill in behind it.