chapter 25 vibrations and waves. vibration – a wiggle in time for example: moving back and forth...
TRANSCRIPT
![Page 1: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/1.jpg)
Chapter 25
Vibrations and Waves
![Page 2: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/2.jpg)
Vibration – a wiggle in time
For example: moving back and forth in the same space, ie., pendulum.
**A vibration exists over time.**
![Page 3: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/3.jpg)
Wave – a wiggle in space andand time
For example: light and sound
**A wave exists over space and time**
![Page 4: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/4.jpg)
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.
![Page 5: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/5.jpg)
Periods
•Periods depend only on 2 things:–The length of the pendulum and
–The acceleration of gravity
![Page 6: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/6.jpg)
Periods•T = period
L= the length of the pendulum g = acceleration of gravity = “pi” 3.14…
T = 2 L/g
![Page 7: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/7.jpg)
Periods
The longer the pendulum, the
greater the period.
![Page 8: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/8.jpg)
25.2 Wave Description
•The back and forth motion of the pendulum (aka “oscillatory motion”) is called simple harmonic motion.
![Page 9: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/9.jpg)
Simple Harmonic Motion
![Page 10: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/10.jpg)
In simple harmonic motion…
the restoring force is proportional to the displacement from equilibrium.
![Page 11: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/11.jpg)
Major parts of a wave:Midpoint (Equilibrium)
![Page 12: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/12.jpg)
Crests and Troughs
Crest (high point)
Trough (low point)
![Page 13: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/13.jpg)
Amplitude - distance from midpoint to crest or trough
![Page 14: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/14.jpg)
Wavelength () – distance from one crest (trough) to the next
![Page 15: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/15.jpg)
Frequency (f)how frequently a vibration occurs
(# of crests per second)vibrations per second
![Page 16: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/16.jpg)
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
![Page 17: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/17.jpg)
Frequency and Period
•Frequency and period are reciprocals of each other.
•Frequency = 1 period•Period = 1 frequency
![Page 18: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/18.jpg)
What is the frequency in v/sec of a 100-hertz wave?
•Answer:a 100 hertz wave vibrates 100 times in 1 second.
![Page 19: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/19.jpg)
What is the period of vibration of a 100-hertz wave?•Answer:period = 1/frequencyperiod = 1/100each period is 1/100 of a second
![Page 20: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/20.jpg)
25.3 Wave Motion
Sound and light waves move.
As waves move, matter is NOT passed along them.
![Page 21: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/21.jpg)
For example:When you create a
wave with a rope, it is the disturbance that
moves along the rope, not the rope itself.
![Page 22: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/22.jpg)
25.4 Wave Speed
How fast a wave moves depends on the
medium of the wave.
![Page 23: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/23.jpg)
Wave speed is related to the frequency and wavelength of the wave.
v = fWave speed (m/s) =
frequency (Hz) X wavelength (m)
![Page 24: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/24.jpg)
Example:What is the speed of a wave with a frequency
of 100 Hz and a wavelength of .025
meters?
![Page 25: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/25.jpg)
Answer:v = fλ
Speed = 100 Hz X .025 m
Speed = 2.5 m/s
![Page 26: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/26.jpg)
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
![Page 27: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/27.jpg)
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
![Page 28: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/28.jpg)
25.7 Interferenceoverlapping waves
Interference pattern: patterns formed when waves overlap
![Page 29: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/29.jpg)
2 types of interference:1.constructive –
reinforcing interference when waves align at the crests and troughs**individual effects are
increased**
![Page 30: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/30.jpg)
Constructive Interference
![Page 31: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/31.jpg)
2.Destructive – cancellation interferencewhen the crest of one wave aligns with the trough of another**their individual effects are reduced**
![Page 32: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/32.jpg)
Destructive Interference
![Page 33: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/33.jpg)
25.8 Standing WavesCaused by interference
![Page 34: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/34.jpg)
Standing WavesIncident wave – initial wave
Reflected wave – wave that reflects back from interference
![Page 35: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/35.jpg)
When aligned, incident and reflected waves form
a standing wave
![Page 36: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/36.jpg)
NODESIn a standing wave,
parts of the rope remain stationary.
These parts are called nodes.
![Page 37: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/37.jpg)
ANTINODESPoints along a wave that occur half way between
nodes.Antinodes are the points
that have the largest amplitude.
Antinodes become the crests & troughs.
![Page 38: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/38.jpg)
NODES and ANTINODES
![Page 39: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/39.jpg)
The Doppler Effect•Christian Doppler (1803-1853)
•Change in frequency due to the motion of a sound source
![Page 40: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/40.jpg)
The Doppler EffectBlue shift = frequency increases as it approachesRed shift = frequency decreases as it leaves
![Page 41: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/41.jpg)
Blue Shift Red Shift
Higher frequency Lower frequency
![Page 42: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/42.jpg)
Galaxies show a red shift in the light they emit.
![Page 43: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/43.jpg)
Bow wavesEX: swimming faster than
the waves you’re producing
![Page 44: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/44.jpg)
Shock waves – 3-dimensional bow wavesEX: a speed boat moves much faster than the waves it produces
![Page 45: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/45.jpg)
SONIC BOOM – the sharp crack heard when the shock wave that sweeps behind a supersonic aircraft reaches the listener.
![Page 46: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/46.jpg)
A slower aircraft sends sound wave crests one at a time and we hear it as a continuous noise.
![Page 47: 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](https://reader036.vdocuments.site/reader036/viewer/2022062305/5697bfa51a28abf838c977a5/html5/thumbnails/47.jpg)
FORMULAS FOR CHAPTER 25:
T = 2 L/gFrequency = 1/periodPeriod = 1/frequency
v = f