![Page 1: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/1.jpg)
PHYSICS
Waves & Simple Harmonic Motion
![Page 2: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/2.jpg)
A repeating back-and-forth motion about an equilibrium position is a vibration.
A disturbance that is transmitted progressively from one place to the next with no actual transport of matter is a wave.
Light and sound are both forms of energy that move through space as waves.
![Page 3: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/3.jpg)
19.1 Vibration of a Pendulum
![Page 4: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/4.jpg)
Two pendulums of the same length have the same period
regardless of mass.
19.1 Vibration of a Pendulum
![Page 5: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/5.jpg)
Simple harmonic motion is the periodic and
repetitive motion of an object.
– a pendulum
– a mass on a spring
– a plucked guitar string
– Satellite orbiting the earth
19.1 Simple Harmonic Motion
![Page 6: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/6.jpg)
Oscillations of Springs
19.1 Simple Harmonic Motion
The force of gravity pulls the
mass toward Earth while the
restorative force of the spring
pulls the mass upward.
From Hooke’s Law, we can
calculate the restorative force
of a spring, Fs.
Fs = kx
![Page 7: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/7.jpg)
Oscillations of Springs
19.1 Simple Harmonic Motion
At equilibrium position, the
restorative force of the spring
is equal in magnitude but
opposite in direction to the
gravitational force:
Fs = Fg
kx = mg
![Page 8: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/8.jpg)
Example
19.1 Simple Harmonic Motion
A 4.0-kilogram mass is suspended by a spring. In its
equilibrium position, the mass has extended the spring
0.10 meters beyond its unstretched length. What is the
spring constant of this spring?
![Page 9: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/9.jpg)
Determining the Period of a Spring
19.1 Simple Harmonic Motion
If the motion of an oscillating spring is graphed versus
time, the resulting function is a sine wave.
![Page 10: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/10.jpg)
19.2 Wave Description
![Page 11: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/11.jpg)
Determining the Period of a Spring
19.1 Simple Harmonic Motion
The period of the spring then, is the time of one complete
cycle.
![Page 12: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/12.jpg)
Oscillating Spring Example
19.1 Simple Harmonic Motion
A 4.0-kilogram mass is suspended from an unstretched
spring. When released from rest, the mass moves a
maximum distance of 0.20 meters before reversing
direction. What are the period and frequency of this
spring-mass oscillator?
![Page 13: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/13.jpg)
Energy in Oscillations
19.1 Simple Harmonic Motion
In an oscillation, energy continually changes form from
potential energy to kinetic energy.
𝐸 = 𝑈 + 𝐾
![Page 14: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/14.jpg)
Energy in Oscillations
19.1 Simple Harmonic Motion
Conservation of energy is often needed to solve oscillation
problems.
𝑈1 + 𝐾1 = 𝑈2 + 𝐾2
1
2𝑘𝑥1
2 +1
2𝑚𝑣1
2 =1
2𝑘𝑥2
2 +1
2𝑚𝑣2
2
𝑚𝑔ℎ1 +1
2𝑚𝑣1
2 = 𝑚𝑔ℎ2 +1
2𝑚𝑣2
2
Spring
Pendulum
![Page 15: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/15.jpg)
19.1 Simple Harmonic Motion
A mass, suspended from a string as shown, is
oscillating between positions I and III. These
positions represent the amplitudes experienced
during the oscillation. Position II is the equilibrium
position and lies midway between positions I and
III.
a) At which position or positions is the useful
potential energy of the oscillation system
zero?
b) At which position or positions is the net force
on the mass the greatest?
c) What is the effect on the period, T, of the
oscillation if mass m is replaced with mass
2m?
![Page 16: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/16.jpg)
The Parts of a Wave
19.2 Wave Description
The high points on a wave are called crests.
The low points on a wave are called troughs.
![Page 17: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/17.jpg)
• The term amplitude refers to the distance from the midpoint
to the crest (or trough) of the wave.
• The amplitude is the maximum displacement from
equilibrium.
19.2 Wave Description
![Page 18: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/18.jpg)
• The wavelength of a wave is the distance from the top of
one crest to the top of the next one.
• Equivalently, the wavelength is the distance between
successive identical parts of the wave.
19.2 Wave Description
![Page 19: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/19.jpg)
Frequency
The number of vibrations an
object makes in a unit of time
is an object’s frequency.
The frequency specifies the
number of back-and-forth
vibrations in a given time
(usually one second).
19.2 Wave Description
![Page 20: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/20.jpg)
The unit of frequency is called the hertz (Hz).
A frequency of one cycle per second is 1 hertz, two cycles
per second is 2 hertz, and so on. Higher frequencies are
measured in
• kilohertz (kHz—thousands of hertz)
• megahertz (MHz—millions of hertz)
• gigahertz (GHz—billions of hertz)
19.2 Wave Description
![Page 21: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/21.jpg)
Electrons in the antenna of an AM radio station at 960 kHz
vibrate 960,000 times each second, producing 960-kHz
radio waves.
19.2 Wave Description
![Page 22: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/22.jpg)
Most information gets to us in some form of wave.
• Sound is energy that travels to our ears in the form of
a wave.
• Light is energy that comes to our eyes in the form of
a different kind of wave (an electromagnetic wave).
• The signals that reach our radio and television sets
also travel in the form of electromagnetic waves.
19.3 Wave Motion
![Page 23: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/23.jpg)
When energy is transferred by a wave from a vibrating source
to a distant receiver, no matter is transferred between the two
points.
19.3 Wave Motion
![Page 24: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/24.jpg)
19.3 Wave Motion
![Page 25: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/25.jpg)
The speed of a wave depends on the medium through
which the wave moves.
Whatever the medium, the speed, wavelength, and
frequency of the wave are related.
19.4 Wave Speed
![Page 26: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/26.jpg)
If the wavelength is 1 meter, and one wavelength
per second passes the pole, then the speed of the
wave is 1 m/s.
19.4 Wave Speed
![Page 27: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/27.jpg)
v = f
Where v is wave speed, is wavelength, and f is
wave frequency.
19.4 Wave Speed
![Page 28: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/28.jpg)
In air, the product of wavelength and frequency is the
same for every frequency of sound.
That’s why you don’t hear the high notes in a chord
before you hear the low notes. The sounds all reach you
at the same time.
Long wavelengths have low frequencies, and short
wavelengths have high frequencies.
19.4 Wave Speed
![Page 29: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/29.jpg)
Wavelength and frequency vary inversely to produce the
same wave speed for all sounds.
19.4 Wave Speed
![Page 30: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/30.jpg)
If a water wave vibrates up and down two times each second
and the distance between wave crests is 1.5 m, what is the
frequency of the wave? What is its wavelength? What is its
speed?
19.4 Wave Speed
![Page 31: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/31.jpg)
If a water wave vibrates up and down two times each second
and the distance between wave crests is 1.5 m, what is the
frequency of the wave? What is its wavelength? What is its
speed?
Answer:
The frequency of the wave is 2 Hz; its wavelength is 1.5 m;
and its wave speed is
19.4 Wave Speed
![Page 32: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/32.jpg)
Whenever the motion of the medium is at right angles to
the direction in which a wave travels, the wave is a
transverse wave.
19.5 Transverse Waves
![Page 33: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/33.jpg)
When the particles oscillate parallel to or along the direction
of the wave, the wave is a longitudinal wave.
19.6 Longitudinal Waves
![Page 34: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/34.jpg)
An interference pattern is a regular arrangement
of places where wave effects are increased,
decreased, or neutralized.
19.7 Interference
![Page 35: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/35.jpg)
In constructive interference, the crest of one wave
overlaps the crest of another and their individual effects
add together.
In destructive interference, the crest of one wave
overlaps the trough of another and their individual effects
are reduced.
19.7 Interference
![Page 36: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/36.jpg)
a. In constructive interference, the waves reinforce each
other to produce a wave of increased amplitude.
19.7 Interference
![Page 37: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/37.jpg)
a. In constructive interference, the waves reinforce each
other to produce a wave of increased amplitude.
b. In destructive interference, the waves cancel each other
and no wave is produced.
19.7 Interference
![Page 38: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/38.jpg)
a. Two overlapping water waves produce an
interference pattern.
19.7 Interference
![Page 39: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/39.jpg)
a. Two overlapping water waves produce an
interference pattern.
b. Overlapping concentric circles produce a pictorial
representation of an interference pattern.
19.7 Interference
![Page 40: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/40.jpg)
Interference patterns are nicely
illustrated by the overlapping of
concentric circles printed on a pair
of clear sheets.
19.7 Interference
![Page 41: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/41.jpg)
A standing wave is a wave that appears to stay in one
place—it does not seem to move through the medium.
19.8 Standing Waves
![Page 42: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/42.jpg)
Certain parts of a standing wave remain stationary.
• Nodes are the stationary points on a standing wave.
Hold your fingers on either side of the rope at a node,
and the rope will not touch them.
• The positions on a standing wave with the largest
amplitudes are known as antinodes.
• Antinodes occur halfway between nodes.
19.8 Standing Waves
![Page 43: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/43.jpg)
19.8 Standing Waves
![Page 44: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/44.jpg)
a. Shake the rope until you set up a standing wave of ½ wavelength.
19.8 Standing Waves
![Page 45: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/45.jpg)
a. Shake the rope until you set up a standing wave of ½ wavelength.
b. Shake with twice the frequency and produce a standing wave of 1
wavelength.
19.8 Standing Waves
![Page 46: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/46.jpg)
a. Shake the rope until you set up a standing wave of ½ wavelength.
b. Shake with twice the frequency and produce a standing wave of 1
wavelength.
c. Shake with three times the frequency and produce a standing wave of
1 ½ wavelengths.
19.8 Standing Waves
![Page 47: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/47.jpg)
19.9 The Doppler Effect
Each circle represents the crest of a wave.
Waves spread out equally in all directions (the concentric circles are evidence of this.)
The frequency of the crests = the frequency of the bug.
![Page 48: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/48.jpg)
19.9 The Doppler Effect
As the bug moves forward, the frequency of the waves in
front of him changes. (Not the wave speed though!)
YX
![Page 49: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/49.jpg)
Sound
The Doppler effect causes the changing pitch of a siren.
19.9 The Doppler Effect
![Page 50: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/50.jpg)
Police use the Doppler effect of radar waves to
measure the speeds of cars on the highway.
19.9 The Doppler Effect
![Page 51: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/51.jpg)
Light
The Doppler effect also occurs for light.
• When a light source approaches, there is an increase in
its measured frequency.
• When it recedes, there is a decrease in its frequency.
19.9 The Doppler Effect
![Page 52: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/52.jpg)
If the bug swims as fast as the
wave speed, it will keep up with the
wave crests it produces.
The bug moves right along with the
leading edge of the waves it is
producing.
19.10 Bow Waves
![Page 53: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/53.jpg)
19.10 Bow Waves
![Page 54: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/54.jpg)
19.10 Bow Waves
![Page 55: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/55.jpg)
v = speed of bug
vw = wave speed
19.10 Bow Waves
![Page 56: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/56.jpg)
A shock wave is a three-dimensional wave that consists of
overlapping spheres that form a cone.
The conical shock wave generated by a supersonic craft spreads
until it reaches the ground.
19.11 Shock Waves
![Page 57: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/57.jpg)
A common misconception is that sonic booms are
produced only at the moment that the aircraft
surpasses the speed of sound.
In fact, a shock wave and its resulting sonic boom are
swept continuously behind an aircraft traveling faster
than sound.
19.11 Shock Waves
![Page 58: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/58.jpg)
The shock wave has not yet
encountered listener C, but is
now encountering listener B,
and has already passed
listener A.
19.11 Shock Waves
![Page 59: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/59.jpg)
• A supersonic bullet passing overhead produces a
crack, which is a small sonic boom.
• When a lion tamer cracks a circus whip, the cracking
sound is actually a sonic boom produced by the tip of
the whip.
• Snap a towel and the end can exceed the speed of
sound and produce a mini sonic boom.
19.11 Shock Waves
![Page 60: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/60.jpg)
An airplane traveling at twice the speed of sound
makes a conical shock wave. What is the angle of
the conical wave?
α
19.11 Shock Waves
![Page 61: PHYSICS Waves & Simple Harmonic Motioncottageschoolphysics.weebly.com/uploads/1/0/2/7/10277901/ch._19_waves_2018feb23.pdf– a plucked guitar string – Satellite orbiting the earth](https://reader033.vdocument.in/reader033/viewer/2022041508/5e26773bc88d5e19dc1b7ea9/html5/thumbnails/61.jpg)
A supersonic aircraft produces a conical shock wave in the
air.
a) If the aircraft flies at 1.5 times the speed of sound, what
is the angle (α) of the conical wave?
b) If the aircraft flies faster, does the angle increase or
decrease?
α
19.11 Shock Waves