Chapter 25 Vibrations and Waves

Vibration – a wiggle in time For example: moving back and forth in the same space, ie., pendulum. **A vibration exists over time.**

and Wave – a wiggle in space and time For example: light and sound **A wave exists over space and time**

25.1 Vibration of a Pendulum Pendulums swing “to and fro” (back and forth) The time of the “to and fro” is called a period.

Periods Periods depend only on 2 things: –The length of the pendulum and –The acceleration of gravity

Periods T = period L= the length of the pendulum g = acceleration of gravity  = “pi”  3.14… T = 2   L/g

Periods  The longer the pendulum, the greater the period.

25.2 Wave Description The back and forth motion of the pendulum (aka “oscillatory motion”) is called simple harmonic motion.

Simple Harmonic Motion

In simple harmonic motion… the restoring force is proportional to the displacement from equilibrium.

Major parts of a wave: Midpoint (Equilibrium)

Crests and Troughs Crest (high point) Trough (low point)

Amplitude - distance from midpoint to crest or trough

Wavelength ( ) – distance from one crest (trough) to the next

Frequency (f) how frequently a vibration occurs (# of crests per second) vibrations per second

Heinrich Hertz Heinrich Hertz demonstrated radio waves in The unit of frequency is the Hertz. 1 vibration per second = 1 Hertz Kilohertz = 1000 v/sec Megahertz = v/sec

Frequency and Period Frequency and period are reciprocals of each other. Frequency = 1  period Period = 1  frequency

What is the frequency in v/sec of a 100-hertz wave? Answer: a 100 hertz wave vibrates 100 times in 1 second.

What is the period of vibration of a 100-hertz wave? Answer: period = 1/frequency period = 1/100 each period is 1/100 of a second

25.3 Wave Motion Sound and light waves move. As waves move, matter is NOT passed along them.

For example: When you create a wave with a rope, it is the disturbance that moves along the rope, not the rope itself.

25.4 Wave Speed How fast a wave moves depends on the medium of the wave.

Wave speed is related to the frequency and wavelength of the wave. v = f Wave speed (m/s) = frequency (Hz) X wavelength (m)

Example: What is the speed of a wave with a frequency of 100 Hz and a wavelength of.025 meters?

Answer: v = fλ Speed = 100 Hz X.025 m Speed = 2.5 m/s

25.5 Transverse Waves Waves produced when the motion of the medium is at right angles to the direction in which the wave travels. EX: a fishing bobber in a lake

25.6 Longitudinal Waves Waves produced when the particles move ALONG the direction of the wave rather than at right angles to it EX: Sound waves

25.7 Interference overlapping waves Interference pattern: patterns formed when waves overlap

2 types of interference: 1.constructive – reinforcing interference when waves align at the crests and troughs **individual effects are increased**

Constructive Interference

2.Destructive – cancellation interference when the crest of one wave aligns with the trough of another **their individual effects are reduced**

Destructive Interference

25.8 Standing Waves Caused by interference

Standing Waves Incident wave – initial wave Reflected wave – wave that reflects back from interference

When aligned, incident and reflected waves form a standing wave

NODES In a standing wave, parts of the rope remain stationary. These parts are called nodes.

ANTINODES Points along a wave that occur half way between nodes. Antinodes are the points that have the largest amplitude. Antinodes become the crests & troughs.

NODES and ANTINODES

The Doppler Effect Christian Doppler ( ) Change in frequency due to the motion of a sound source

The Doppler Effect Blue shift = frequency increases as it approaches Red shift = frequency decreases as it leaves

Blue ShiftRed Shift Higher frequency Lower frequency

Galaxies show a red shift in the light they emit.

Bow waves EX: swimming faster than the waves you’re producing

Shock waves – 3-dimensional bow waves EX: a speed boat moves much faster than the waves it produces

SONIC BOOM – the sharp crack heard when the shock wave that sweeps behind a supersonic aircraft reaches the listener.

A slower aircraft sends sound wave crests one at a time and we hear it as a continuous noise.

FORMULAS FOR CHAPTER 25: T = 2   L/g Frequency = 1/period Period = 1/frequency v = f