Vibrations, Waves, & Sound
Chapters 25 & 26
25.1 Vibration of a Pendulum
• The period of the pendulum depends
only on the length of a pendulum and
the acceleration of gravity.
Period
• The time it takes for one complete cycle of
motion.
• Represented by the symbol T
• Unit of seconds
Frequency
• The number of cycles completed in a unit of
time (usually seconds)
• Represented by the symbol f
• Unit of s-1 (also known as Hertz)
Period and Frequency
• Period and frequency are inversely related.
• f = 1/T and T = 1/f
A plucked string vibrates back and forth10
times each second.
• What is the period?
1/10 s
What is the frequency?
10 cycles per second (10 Hz)
What is a wave?
• A wave is an means by which energy is
transferred from one place to another via
periodic disturbances
Waves transfer energy
• Note that, while energy is transferred from point A to
point B, the particles in the medium do not move
from A to B.
– Individual particles of the medium merely vibrate
back and forth in simple harmonic motion
• The rate of energy transfer is proportional to
the square of the amplitude
– When amplitude is doubled, the energy carried
increases by a factor of 4.
25.2 Wave Description
• The source of all waves is something that
vibrates.
• The back-and-forth vibratory motion of a
swinging pendulum is called
simple harmonic motion.
25.2 Wave Description
• A sine curve is a pictorial representation of a
wave.
Wave Parts
• Amplitude - the maximum displacement from
equilibrium.
• The high points on a wave are called crests.
• The low points on a wave are called troughs.
• The wavelength of a wave is the distance from one
part of a wave to the next identical part.
25.3 Wave Motion
• When energy is transferred by a wave from a
vibrating source to a distant receiver, no
matter is transferred between the two points.
Mechanical Waves
• Waves that require a physical medium to travel
through.
• Examples of physical media are water, air, string,
slinky.
Electromagnetic waves
• Waves that do not require a physical medium.
• Comprised of oscillating electric and magnetic fields
• Examples include x-rays, visible light, radio waves,
etc.
25.4 Wave Speed
• You can calculate the speed of a wave by
multiplying the wavelength by the
frequency.
Wave speed
• Wave speed is determined completely by
the characteristics of the medium
– For an unchanging medium, wave speed is
constant
25.4 Wave Speed
think!
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 3 m/s.
25.5 Transverse Waves
• Particles of the medium move perpendicular to the
direction of energy transfer
• You should be able to identify crests, troughs,
wavelength (distance traveled during one full cycle),
and amplitude
Crest
Trough
25.6 Longitudinal Waves
• Particles of the medium move parallel to the
direction of energy transfer
• Be able to Identify compressions, rarefactions,
wavelengths
Compressions
Rarefactions
25.7 Interference
• The combination of two or more waves in a
medium at the same time.
– Matter cannot occupy the same space at the same
time, but energy can.
25.7 Interference
• The Superposition Principle describes what
happens when waves interfere…
– Waves (energy) pass through each other
completely unaffected
– The medium will be displaced an amount equal to
the vector sum of what the waves would have
done individually
Constructive Interference
-pulses to same
side of equilibrium
-resulting medium
displacement is
greater than original
waves
-pulses continue
unaffected
Destructive Interference
• Pulses on opposite
sides of equilibrium
• Resulting displacement
is less than at least
one of the originals
• Pulses continue
unaffected
Complete Destructive Interference
Interference patterns
• Out of phase –
destructive
interference
• In phase –
constructive
interference
25.8 Standing Waves
• A wave pattern that results when two waves of the
same frequency, wavelength, and amplitude travel in
opposite directions and interfere.
25.8 Standing Waves
• Only certain frequencies produce standing wave
patterns.
25.8 Standing Waves
•Nodes are areas of complete destructive interference
and have no displacement
•Antinodes are areas of constructive interference and
have maxiumum displacement
25.9 The Doppler Effect
• As a wave source approaches, an observer
encounters waves with a higher frequency.
As the wave source moves away, an observer
encounters waves with a lower frequency.
25.9 The Doppler Effect
• The greater the speed of the source, the
greater will be the Doppler effect.
• Family Video
25.9 The Doppler Effect
• The Doppler effect also occurs for light.
• When a light source approaches, there is an
increase in its measured frequency (blue shift)
• When it recedes, there is a decrease in its
frequency (red shift)
26.1 The Origin of Sound
• All sounds originate in the
vibrations of material objects.
• Pitch is the human perception of
frequency
26.1 The Origin of Sound
• The normal range of human hearing is 20 to
20,000 hertz.
• Sound waves with frequencies below 20 hertz
are called infrasonic.
• Sound waves with frequencies above
20,000 hertz are called ultrasonic.
26.2 Sound in Air
• Consider sound waves in a tube.
• When the prong of a tuning fork next to the tube
moves toward the tube, a compression enters the
tube.
• When the prong swings away, in the opposite
direction, a rarefaction follows the compression.
• As the source vibrates, a series of compressions
and rarefactions is produced.
26.3 Media That Transmit Sound
• The speed of sound differs in different
materials.
• In general, sound is transmitted faster in
liquids than in gases, and still faster in solids.
• Sound cannot travel in a vacuum.
• Bell in vacuum
26.4 Speed of Sound
• The speed of sound depends on the
characteristics of the medium. A material’s
temperature, mass of particles, density, and
elasticity are all factors.
– Helium & Sulfur Hexafluoride
- In room temperature air, sound travels about 340 m/s
- In water, sound travels about 1200 m/s
- In aluminum, sound travels about 5000 m/s
26.6 Natural Frequency
• When any object composed of an elastic
material is disturbed, it vibrates at its own
special set of frequencies, which together
form its special sound.
26.7 Forced Vibration
• Sounding boards are an important part of all
stringed musical instruments because they
are forced into vibration and produce the
sound.
26.8 Resonance
• If the frequency of a forced vibration
matches an object’s natural frequency,
resonance dramatically increases the
amplitude.
• Resonance occurs whenever
successive impulses are applied to a
vibrating object in rhythm with its
natural frequency.
Resonance Videos
• How to Break a Glass
• Jaime Vendera
• Tacoma Narrows Bridge
Reflection
• The bouncing of a wave when it encounters
the boundary between two different media
Fixed End Reflection
• At a fixed boundary, waves are inverted as they are
reflected.
Free End Reflection
• At a free boundary, waves are reflected on the same
side of equilibrium