UNIT 1:
mechanical waves / sound
Properties of waves, example of waves (sound. Light, seismic),
Reflection, Doppler effect, shock wave, diffraction, refraction,
Interference, resonance, standing waves, Physics of music,
More on sound.
Chapter 16 in Cutnell, Johnson: Physics, 8th Edition
Oscillations can travel through medium such as water and air without carrying
Matter along. These mechanic disturbances are called waves.
Oscillation around an equilibrium position
1. waves/intro
2. wave on a string
3. sound waves
http://www.acs.psu.edu/drussell/Demos/waves-intro/waves-intro.html
http://www.walter-fendt.de/ph14e/springpendulum.htm
2
Part1 : Waves —
types and properties
●
A wave is a traveling disturbance
consisting of coordinate vibrations that
transmit energy with not net movement
of matter.
The disturbance is frequently called an
oscillation or vibration.
The substance through which the wave
travels is called the medium.
The location of the energy is moving but there is no transfer of medium.
A wave acts like a particle.
3
Imagine you are floating in the ocean and you are hit by
Waves. You go up and down as waves pass you.
It 10 waves pass you in 1 second that means
10 cycles per second.
This is the
frequency
. The unit is Hertz.
Since there are 10 cycles per second, this means each cycle (up,down,up)
Lasts 1/10 = 0.1 second. This is the period. Unit is second.
So
period = 1/frequency
As the waves pass you, you can measure the distance between 2 crests.
This is the wavelength. The unit is meter. The maximum distance you reach
Above the calm is is the amplitude. Unit is meter. The energy of the wave
(a wave can do damage, break things) is proportional to the intensity
16.2
Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is related to the period and has units of Hz, or s
-1.
T
5
Waves — types and
properties
- again
●
The amplitude of a wave is the
maximum displacement of the wave
from the equilibrium position.
It is just the distance equal to the height of
Waves — types and
properties
, cont’d
The wavelength is the distance between
successive “like” points on a wave.
“Like” points might be peaks, valleys, etc.
The wavelength is denoted by the Greek
Compare the waves:
Here is an illustration of
changing the wavelength
and/or amplitude.
Lower amplitude implies
smaller height/depth
Shorter wavelength
implies more complete
waves “fit” in a given
distance
Waves — types and
properties
, cont’d
This figure illustrates the two main types of
waves.
Discuss
http://phys23p.sl.psu.edu/phys_anim/waves/creating_Long.avi
http://phys23p.sl.psu.edu/phys_anim/waves/creating_Trans.avi
Waves — types and
properties
, cont’d
There are two main wave types:
Transverse waves have oscillations that are
perpendicular (transverse) to the direction the
wave travels.
Examples include waves on a rope,
electromagnetic waves, and some seismic
waves.
Longitudinal waves have oscillations that are
along the direction the wave travels.
Examples include sound and some seismic
waves.
Waves — types and
properties
, cont’d
We use different terminology for the “peaks”
and “valleys” of a longitudinal wave.
A compression is where the medium is squeezed
together.
11
●Typically we represent a sound wave as a transverse wave (even
though it is not). Sound wave = air pressure changes with time.
A region of compression is drawn as a crest.
A region of expansion is drawn as a trough.
16.5
The Nature of Sound Waves
The distance between adjacent condensations is equal to the
wavelength of the sound wave.
16.5
The Nature of Sound Waves
14
Another example: Visible light is an electromagnetic wave.
Light can travels in a vacuum.
Each color is a given wavelength and a given frequency
Frequency x wavelength = speed of light
(186,000 miles/s in a vacuum)
Light is an electric field and a magnetic field oscillating in the vacuum, the same
Way sound wave is air pressure oscillating and seismic wave is stretching or
Twisting of rocks.
15
Another example: Seismic wave traveling in Earth.
Waves — types and
properties
, cont’d
The wavelength and frequency are related to
the wave speed according to:
v=
λ
f
v is the wave’s speed
f is the wave’s frequency
λ
is the wave’s wavelength
Example
Before a concert, musicians in an orchestra
tune their instruments to the note A, which
has a frequency of 440 Hz. What is the
wavelength of this sound in air at room
temperature?
The speed of sound at this temperature is
344 m/s.
18
You have waves in gas (sound)
Wave in the vacuum (light)
Wave in solid (Earthquake wave)
Wave on liquid (water wave)
Wave along 1 line (slinky, rope)
Wave a long a surface 2D (ripples in water)
Wave in 3D (sound)
19
A WAVE pulse
A wave can be short and fleeting
Like the burst of a balloon, a tsunami,
Light from a camera.
A wave can be continuous
= train of pulses.
Example The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric and
magnetic field disturbances traveling at a speed of 3.00x10
8m/s. A station
broadcasts AM radio waves whose frequency is 1230x10
3Hz and an FM
radio wave whose frequency is 91.9x10
6Hz. Find the distance between
adjacent crests in each wave.
The atmosphere absorbs most of the wavelengths shorter than ultraviolet, most of the
wavelengths between infrared and microwaves, and most of the longest radio waves.
The radio window consists of frequencies which range from about 5 MHz (5 million hertz) to 30 GHz (30 billion hertz). The low-frequency end of the window is limited by signals being reflected by the ionosphere back into space, while the upper limit is caused by absorption of the radio waves by water vapor and carbon dioxide in the atmosphere. As atmospheric conditons change the radio window can expand or shrink. On clear days with perfect conditions signals as high as 300GHz have been detected.
21
EXAMPLES
Speed of a wave = distance / time = wavelength (m) / period(s)
And period = 1/ frequency
Frequency is the number of cycles per second
And period is the time a cycle lasts in seconds.
Source: The physics of every day phenomena. Griffith. Mc Graw Hill.
1. Suppose that water waves coming into a dock have a velocity of 1.2m/s and a wavelength
Of 2.4m. With what frequency do these waves meet the dock ?
2. Suppose the water waves have a wavelength of 1.4, and a period of 0.8s.
What is the velocity of these waves ?
3. A longitudinal wave on a slinky has a frequency of 5Hz and a speed of 2m/s.
What is the wavelength of this wave?
4. A wave on a string has a speed of 12m/s and a period of 0.4s
A)What is the frequency of the wave /
B)What is the wavelength of the wave
5. A wave on a rope is shown below. Find the wavelength.
If the frequency is 2Hz, what is the wave speed ?
Part2 : waves on a string
Consider a string of length l and mass m.
The speed at which a wave travels on the
string when it is under a tension T is
ρ
is the mass per unit length:
ρ
=mass of the string/length of the string
more mass = more inertia = more resistance
to motion. More tension = more force.
v
= Τ
ρ
.
See exploration of physics . See how speed depends on tension and on
Inertia. See effect of fixed or free end.
Waves — types and
properties
, cont’d
From this we see that the speed:
Increases as the tension increases
The string has a greater restoring force that
attempts to straighten it out.
Is faster for smaller strings
The string has less mass that has to be moved by
the restoring force.
Is independent of the length
The speed depends on the mass per length, not
on just the length.
Example
A student stretches a Slinky out on the floor to a
length of 2 meters. The force needed to keep
the Slinky stretched in measured and found to
be 1.2 newtons. The Slinky’s mass is
0.3 kilograms. What is the speed of any wave
sent down the Slinky by the student?
First step collect data:
L=2m
T=1.2N
m= 0.3 kg Solve for V
Density = mass/length in kg per m
v
= Τ
ρ
.
16.3
The Speed of a Wave on a String
Example 2 Waves Traveling on Guitar Strings
Transverse waves travel on each string of an electric guitar after the
string is plucked. The length of each string between its two fixed ends
is 0.628 m, and the mass is 0.208 g for the highest pitched E string and
3.32 g for the lowest pitched E string. Each string is under a tension
of 226 N. Find the speeds of the waves on the two strings.
16.3
The Speed of a Wave on a String
High E
(
0.208
10
kg
)
(
0.628
m
)
826
m
s
N
226
3 -=
×
=
=
L
m
F
v
Low E
(
3.32
10
kg
)
(
0.628
m
)
207
m
s
N
226
3 -=
×
=
=
L
m
F
v
Problems:
1. A certain rope has a length of 8m and a mass of 2.4kg. It is fixed at one end and held taut the other with a tension of 30N. The end of the
Rope is moved up and down with a frequency of 2.5Hz. A. What is the mass per unit length of the rope ?
B)What is the speed of waves on this rope ?
C) What is the wavelength of waves on this rope having a frequency of 2.5Hz ? D) How many complete cycles of these waves will fit on the rope ?
E) How long does it take for the leading edge of the waves to reach the other end Of the rope and start coming back?
2. Suppose that a guitar string has a length of 8.8m A mass of 0.12kg and a tension of 135N..
A. What is the mass per unit length of this string ? B) What is the speed. Of a wave on this string ?
3. A wave has a speed of 12m/s and a period of 0.4s. A0 What is the frequency of the wave ?
PART 3: SOUND is a WAVE / speed of sound.
Sound is a disturbance that travels at a speed of 340m/s
At room Temperature. Or 1 mile in 5 seconds
Or 1000 feet in 1 second. By comparison :
Light covers 1 foot in 0.000000001 s (10
-9
s)
We worked on the speed of a wave in a string.
What about the speed of sound ?
The speed of sound in air = speed of molecules
(they have a jiggling motion or random motion due to
The temperature. They have kinetic energy ).
Increase the temperature and the speed Increases too.
(see applet exploration of physical sciences, 3 phases of matter)
Temperature is a measure of their kinetic energy.
T is proportional to mV
2
(average kinetic energy
of molecule). When T = absolute 0 = - 273C,
the molecules Can't move anymore.
Try to write a relationship between the speed of sound
And the temperature.
http://www.physics.ucla.edu/demoweb/ntnujava/gas2D/ebrownian_motion.htm
Brownian motion explained in 1905 by Einstein = the air molecules
30
●
The speed of a sound wave when the
air is at a temperature T is
The temperature must be in Kelvin.
T in kelvin = Celsius + 273
v
= 2 0 .1 ×
Τ
.
That's because the speed of sound = speed of the molecules make up the medium
Carrying the sound. Temperature is a measure of the kinetic energy of the
Molecules. So T is proportional to KE=0.5mv
2So v is proportional to the
Square root of T/
31
DISCUSSION:
The factor of 20.1 depends on the properties
of air.
For other gases:
Helium:
Carbon dioxide:
v
= 5 8 .8 ×
Τ
.
v
= 1 5 .7 ×
Τ
.
So why do your voice change when you inhale helium ?
(bad idea)
32
A little ( ) about temperature scales
33
Example
What is the speed of sound in air at room
temperature (20ºC = 68ºF)?
Convert temperature to kelvin.
The Speed of Sound in medium depend on the “ recoil” force of molecules
and their mass density. Like a wave on a rope,
LIQUIDS
SOLID BARS
ρ
ad
B
v
=
ρ
Y
v
=
Assignments:
v
= 2 0 .1 ×
Τ .
v
= Τ
ρ
.
v=frequency x wavelength
V is the speed of a sound wave
Traveling in air at the temperature
T. T is in kelvins = celsius +273
V is the speed of a mechanic wave traveling
On a rope of linear density ϼ (m/s) . The force
T (N) was exerted on the rope by the source
Of the wave.
This is true for any kind of wave.
Frequency is the number of cycles per seconds.
Do the problems from next slide. Ref = inquiry to Physics
SEE HINTS:
- convert degrees to kelvin first
- 3.5 million Hz = convert to Hz (1 million = 1,000,000 )
- Speed of sound in human tissue=1500m/s (about speed in water)
- speed of water = 1500m/s
- linear density = length /mass
- convert cm to m (divide by 100)
- MHz means 1,000,000 Hz
37
1.2 children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 3m long. Its mass is 0.5kg, and the force exerted on it by the children is 40N.
A) What is the linear mass density of the rope? B) What is the speed of the waves on the rope ?
2. The force stretching the D string on a certain guitar is 150N. The string's linear mass density is 0.005kg/m What is the speed of waves on the string ?
3. What is the speed of sound in air at the normal boiling temperature of water ?
4. The coldest and hottest temperatures ever recorded in the united States are -83F (210K) and 135F (330K) respectively. What is the speed of sound in air at each temperature ?
5. A 4Hz a continuous wave travels on a slinky. If the wavelength of 0.5m, What is the speed of waves on the slinky?
6. A 500Hz sound travels through pure oxygen. The wavelength of the sound is measured to be 0.65m. What is the speed Of sound in oxygen /
7. A wave traveling 80m/s has a wavelength of 3.2m. What is the frequency of the wave ?
8. What frequency of sound traveling in air at 20C has a wavelength equal to 1.7m, the average height of a person ?
9. What is the wavelength of 3.5 million Hz ultrasound as it travels through human body 10. The frequency of middle C on the piano is 261.6 Hz
A) What is the wavelength of sound with this frequency as it travels in air at room temperature B) What is the wavelength of sound with this frequency in water ?
11. A steel cable with total length 30m and mass 100kg is connected to 2 poles. The tension in the cable is 3,000N And the wind makes the cable vibrate with a frequency of 2Hz. Calculate the wavelength of the resulting
38
12. In a student laboratory exercise, the wavelength of a 40,000Hz ultrasound wave is measured to be 0.868cm Find the air temperature.
15. Ultrasound probes can resolve structural details with sizes approximately equal to the wavelength of the Ultrasound wave themselves. What is the size of the smallest feature observable in the human tissue examined With a 20MHz ultrasound, The speed of sound in human tissue is 1540m/s,
16. A sonic depth gauge is placed 5m above the ground.
An ultrasound pulse sent downward reflects off snow and reaches the device 0.03 seconds after it was emitted. The air temperature is -20C.
A0 How far is the surface of the snow from the device ? B) How deep is the snow?
DRAW TO GET IT. Not HARD. FROM INTRO physics BOOK.
17. The huge volcanic eruption on the island of Krakatoa, Indonesia, In 1883 was heard on Rodriguez Island, 4,782 km (2 970 miles) away. How long did it take the sound to travel to Rodriguez?
18. A baseball fan sitting in the : cheap seats”is 150m from home plate.
How much time elapses between the instant the fan sees a batter hit the ball and the moment the fan hears the sound ? 19. A geologist is camped 8,000 m (5 miles) from a volcano as it erupts.
A) How much time does it take the seismic waves produced by the eruption to reach the geologist's camp assuming the waves travel through granite as sound waves do ? (google speed of sound in granite)
20. A sound emitted underwater reflects off a school of fish and is detected at the sameplace 0.01s later. How far away are the fish ? (look for speed of sound in water)
