PHYS 1114: Physics I
Lecture 11:
Waves, Sound, & Light
Professor Kenny L. Tapp
Simple Harmonic Motion
Waves
• Waves&are&disturbances&(energy)&that&
propagate&(move)&
• Waves&involve&a&oscilla8on&of&something&
about&an&equilibrium&point
– Pendulum(swinging
– Block(and(Spring(oscilla5ng
– Air(Molecules
– Electric(and(Magne5c(fields
Wave Motion
Displacement (x) is the directed distance of the
object from equilibrium.
A wave pulse is a disturbance
that propagates through a
medium. It transfers energy
without transferring matter;
the energy is a combination
of kinetic and potential
energy.
Amplitude (A) is the maximum displacement.
Period (T) is the time for one full cycle.
Frequency (f) is the number of full cycles per second.
SI unit of frequency: hertz, Hz
1 Hz = 1 cycle/second
Wave Motion
Wave Motion
• Longitudinal
–&par8cle’s&oscilla8on&is&parallel&to&the&pulse’s&mo8on.
Examples:&Sound&waves,&P&waves&in&earthquakes
• Transverse
–&par8cle’s&oscilla8on&is&perpendicular&to&the&pulse’s&mo8on.&
Examples:&Light&waves,&sin&waves,&S&waves&in&earthquakes
• Longitudinal
• Transverse
Wave Motion
Wave Motion
Relationship between wave speed, wavelength,
‣ Parts
period, and frequency:
• Crest
• Trough
‣ Measurements of a wave
• Wave height – the distance between a trough and a
crest
• Wavelength – the horizontal distance between
successive crests (or troughs)
• Wave period – the time interval for one full wave to
pass a fixed position
Quick Question 1
Wavelength & Frequency
Short wavelength
High frequency
Long wavelength
Low frequency
A car driving along a highway at a speed of 23
m/s strays onto the shoulder. Evenly spaced
parallel grooves called “rumble strips” are
carved into the pavement of the shoulder. Rolling
over the rumble strips causes the car’s wheels to
oscillate up and down at a frequency of 82 Hz.
How far apart are the centers of adjacent
rumble-strip grooves?
Wavelength&increases&=&Frequency&decreases
Quick Question 1 ...
We can think of the rumble strips as a wave carved
into the surface of the road. The wave is stationary
relative to the road, but its speed v relative to the car
is equal to the car’s speed v relative to the road. The
frequency f of the wave is equal to the frequency of
the wheel vibrations caused by the wave. The distance
between the centers of adjacent grooves, then, is the
wavelength of the rumble-strip wave.
Quick Question 2
Tsunamis are fast-moving waves often generated by
underwater earthquakes. In the deep ocean their
amplitude is barely noticeable, but upon reaching shore,
they can rise up to the astonishing height of a six-story
building. One tsunami, generated off the Aleutian islands
in Alaska, had a wavelength of 750 km and traveled a
distance of 3700 km in 5.3 h. (a) What was the speed (in
m/s) of the wave? For reference, the speed of a 747
jetliner is about 250 m/s. Find the wave’s (b) frequency
and (c) period.
Quick Question 2 ...
Wave Properties
(a)
(b)
!
This is an illustration of
interference, using the principle of
superposition. The displacement of
any point on the rope is the sum of
the individual displacements:
(c)
Wave Properties
Waves in Oklahoma
If the combined wave is larger than the individual ones, the
interference is constructive; if smaller, it is destructive.
Waves in Oklahoma
Waves in Oklahoma
Waves in Oklahoma
• Create or observe waves in a fluid. Take a picture of the
waves and label these parts of the wave that you
photographed: crest, trough, wavelength, wave height.
• Additionally, take the following measurements of the
waves that you are observing or creating and include that
information on your picture: wavelength, wave height,
wave period, wave frequency.
• Also observe and document an example of wave
interference.
• You may work as a team to accomplish this, but you will
need to document who you worked with on your individual
submission.
19
Standing Waves & Resonance
When a string stretched between two
fixed points is plucked it vibrates in
what is know as its fundamental mode
of vibration (aka the first harmonic).
Nodes
A standing wave is a pattern
which results from the
interference of two or more
waves traveling in the same
medium.
Antinodes
When an integral number of
half-wavelengths fit on the
rope, the frequency is called
the resonant frequency.
Standing Waves & Resonance
Standing Waves & Resonance
Standing waves don't go anywhere, but they do have regions
where the disturbance of the wave is quite small, almost zero.
These locations are called nodes. There are also regions where
the disturbance is quite intense, greater than anywhere else in the
medium, called antinodes.
Standing Waves & Resonance
• For a given harmonic, the wavelength, λ, may be written: λ = 2l ,
n
where l is the length of the string between the fixed endpoints and n
is the number of loops in the string.
• The velocity of a wave may be expressed as the product of its
wavelength and frequency: v = λf . The velocity of a wave is the
speed at which a fixed point on the wave propagates through the
medium in which the wave is traveling. For a wave traveling down a
string the velocity may be expressed: v = 2lf .
n
Natural frequencies for a stretched string:
Quick Question 3
Natural wavelengths can be varied by:
+ varying the length of a string, such as in a piano or harp;
+ varying the mass per unit length of a string, as in a guitar;
+ varying the tension, which is done for fine tuning.
Driving a system at its natural frequency produces resonance.
The wave speed is given by
where FT is the tension and µ is the mass per unit length.
• A 50 m long string has a mass of 0.010 kg. A 2.0 m
segment of the string is fixed at both ends and when a
tension of 20 N is applied to the string, three loops are
produced. What is the frequency of the standing wave?
Sound Waves
Ultrasonic waves are too high in
frequency for human ears. Dogs, cats,
and bats can hear higher frequencies.
Infrasonic waves have frequencies too
low for human ears. They are
produced by earthquakes and other
natural phenomena; elephants and
cows can hear certain frequencies.
The$Speed$of$Sound:$$FIREWORKS
The Speed of Sound
Speed of sound in a solid:
Y is Young’s modulus and ρ is the density.
Speed of sound in a liquid:
B is the bulk modulus.
Speed of sound in dry air:
The$Speed$of$Sound:$$FIREWORKS
July 4, 2011
10:05pm
Air Temperature (Celsius)
v = 331 + (0.6Tc) = 331 + (0.6)(30) = 349 m/s
The$Speed$of$Sound:$$FIREWORKS
Determine the distance that Prof.
Tapp was watching the fireworks
from on July 4, 2011.
Vsound = d / t
Quick Question 4
• The speed of an ultrasonic sound of frequency 45 kHz in
air is 342 m/s.
(a) What is the air temperature?
(b) What is the wavelength of the sound wave?
Visible light
occupies only
a tiny sliver of
the full
spectrum.
Sound$Intensity$and$Sound$Intensity$Level
We perceive sound intensity as loudness; the minimum detectable sound
has an intensity of about 1.0 × 10–12 W/m2, and the threshold of pain
occurs at an intensity of about 1.0 W/m2.
A doubling of loudness corresponds to an increase in intensity of about a
factor of 10.
Sound intensity is measured on a logarithmic scale, in decibels:
ENERGY
The Doppler Effect
The Doppler Effect
As a car or train horn approaches you and then passes by, the pitch of the sound
first rises and then falls. This is called the Doppler effect.
The Doppler Effect
The Doppler Effect
Quick Question 5
• A cop car drives at 30 m/s toward the scene of a crime, with its siren
blaring at a frequency of 2000 Hz. At what frequency do people
hear the siren as it approaches? At what frequency do they hear it as
it passes? The speed of sound in the air is 343 m/s.
Moving Toward:
Moving Away:
Quick Question 5...
Moving Toward:
Moving Away: