chapter 25 vibrations and waves. vibration – a wiggle in time for example: moving back and forth...
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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.**
Wave – a wiggle in space andand 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 HertzHeinrich Hertz demonstrated
radio waves in 1886.The unit of frequency is the
Hertz.1 vibration per second = 1 Hertz
Kilohertz = 1000 v/secMegahertz = 1000000 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/frequencyperiod = 1/100each 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 = fWave 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 itEX: Sound waves
25.7 Interferenceoverlapping 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 interferencewhen the crest of one wave aligns with the trough of another**their individual effects are reduced**
Destructive Interference
25.8 Standing WavesCaused by interference
Standing WavesIncident wave – initial wave
Reflected wave – wave that reflects back from interference
When aligned, incident and reflected waves form
a standing wave
NODESIn a standing wave,
parts of the rope remain stationary.
These parts are called nodes.
ANTINODESPoints 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 (1803-1853)
•Change in frequency due to the motion of a sound source
The Doppler EffectBlue shift = frequency increases as it approachesRed shift = frequency decreases as it leaves
Blue Shift Red Shift
Higher frequency Lower frequency
Galaxies show a red shift in the light they emit.
Bow wavesEX: swimming faster than
the waves you’re producing
Shock waves – 3-dimensional bow wavesEX: 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/gFrequency = 1/periodPeriod = 1/frequency
v = f
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