Wave
A disturbance that propagates in a medium
Disturbance
The wave is a disturbance in the water
Wavelength
In a wave, the distance between the crests (or the distance between the troughs) is called the wavelength (?) of the wave
Amplitude
while the height of the wave is the called the amplitude (A)
Frequency
Another important characteristic of a wave not shown in Figure 11.1 is frequency (f) . The frequency of a wave tells you how many waves hit a certain point every second. Frequency and wavelength are related to one another through the speed of the wave:
Transverse Wave
A wave whose propagation is perpendicular to its oscillation
Longitudinal Wave
A wave whose propagation is parallel to its oscillation
Compressions
Notice that parts of it are bunched up. Those regions are called compressions , and they are the crests of the wave
Rarefactions
The parts of the Slinky � that are spread out are called rarefactions , and they are the troughs of the wave. The distance between the crests (or the troughs) is the wavelength of the wave.
Pitch/volume
This interpretation involves many factors, including the pitch of the sound and the volume .
Sound Waves
1. Sound waves are longitudinal.
2.
The frequency (or wavelength) is the primary factor that determines the pitch.
3.
The amplitude determines the volume.
Equation
There is a rather simple equation that relates the temperature of the air and the speed of sound waves traveling through it:
Droppler effect
The fact that the pitch of the sounds you hear is related to the frequency of the sound waves leads to an interesting phenomenon known as the Doppler effect
Equation
The Doppler effect is reasonably easy to calculate. It depends only on the true frequency of the sound wave (in other words, the pitch you would hear if neither you nor the source of the sound were moving), the speed of the observer, and the speed of the
liquids
Why, then, does sound travel faster in the solids listed than in the liquids listed? Because the speed of sound in a substance also depends on how easily the substance is compressed. The easier it is to compress the substance, the slower sound travels in
Sonic
The human ear, though elegantly designed, cannot detect all frequencies of sound waves. In general, human ears are sensitive to waves whose frequency is between 20 Hz and 20,000 Hz. Waves with these frequencies are called sonic (sahn' ik) waves
Ultrasonic
Waves with frequencies higher than 20,000 Hz are called ultrasonic (uhl' truh sahn' ik) waves
Infrasonic
Waves with frequencies below 20 Hz are called infrasonic (in' fruh sahn' ik) waves.
The speed of light
The speed of light in air (to two significant figures) is 3.0 x 10 8 m/sec.
mediums
The speed of light waves changes depending on the medium through which they travel. Generally speaking, as the medium gets more dense, light waves slow down
Diffraction
The spreading of waves around an obstacle
Coherent
Unlike most individual light sources, however, the light from the two slits is coherent , which means that the spatial relationship between the crests and troughs of one wave compared to those of the other wave does not change.
Wave Interference
They will cancel each other out, so that there is no wave at all. This phenomenon is called wave interference , and it can occur whenever two waves overlap with one another.
Constructive Interference
As a point of terminology, when the waves overlap so that their crests and troughs add together to make larger crests and troughs, it is called constructive interference , because the waves add together to construct a bigger wave.
Destructive interference
When the waves overlap so that their crests and troughs cancel one another out, it is called destructive interference , because the waves destroy one another.
Ether
As a point of terminology, when the waves overlap so that their crests and troughs add together to make larger crests and troughs, it is called constructive interference , because the waves add together to construct a bigger wave
Maxwell's Equations
In 1873, the great physicist James Clerk Maxwell had already derived a series of equations which today we call Maxwell's Equations . Although the implications of his equations were not understood until later, they were recognized as important because they
Electromagnetic force
Now please understand how important this is. Maxwell's equations, which unify electric and magnetic forces into a single electromagnetic force , specify that this force is mediated by a wave whose speed is a direct result of the mathematics. That speed is
Electromagnetic wave
It took physicists a while to realize the implication, but Maxwell's equations tell us that light is an electromagnetic wave . What does that mean? It means that light waves are oscillating electric and magnetic fields
Electromagnetic spectrum
Of course, like any other wave, an electromagnetic wave can have a wide range of wavelengths. As a result, there are many wavelengths in the electromagnetic spectrum . Thus, the broader term for light is simply "electromagnetic wave," and the light that w
Photoelectric effect
Of course, like any other wave, an electromagnetic wave can have a wide range of wavelengths. As a result, there are many wavelengths in the electromagnetic spectrum . Thus, the broader term for light is simply "electromagnetic wave," and the light that w
Photoelectrons
These electrons are typically called photoelectrons , because they come as a result of light shining on metal
Work function
Typically, physicists use the term work function to refer to the energy with which a metal holds on to its electrons. If an electron could absorb enough energy so that it had more energy than the work function of the metal, the electron could break free o
Details of photoelectric effect
1. Electrons were ejected within a few billionths of a second after the light was turned on.
2.
The intensity of the light had no effect on the energy of the electrons after they left the metal. The more intense the light, the greater number of electrons, but the energy of the electrons was independent of the light intensity.
3.
Each metal had a unique "cutoff" frequency. If the light used was below this frequency, electrons would not be emitted.
4.
The maximum kinetic energy of the emitted electrons was directly proportional to the frequency of the light used.
Photons
He assumed that light came in little "electromagnetic bundles" called photons (foh' tahns), and that the energy of each photon was proportional to the frequency of the light, according to the following equation:
Planck's constant
In this equation, "E" is the energy of the light; "f" is its frequency; and "h" is a fundamental constant in nature which is now known as Planck's constant , after Max Planck, a German physicist. The value of the constant is 6.63 x 10 -34 J�sec.
Electron volt
Thus, it is more convenient to use a small unit for energy when dealing with light. That unit is called the electron volt (abbreviated as eV ). You will learn the actual definition of the electron volt in a later module. For right now, I will just give yo
Particle-wave duality
Even today, we do not have a really good answer to that question. Thus, we "fudge" the explanation by giving this phenomenon a name. We say that this illustrates the particle-wave duality of light. In some situations, we can best describe light as a wave.
James Clerk Maxwell
Maxwell developed equations that unified the electric and magnetic force into the electromagnetic force.
Albert Einstein
He is best known for his special and general theories of relativity, which form the basis of much of the physics that us done today.
Virtual image
An image formed as the result of extrapolating light beams
Concave
When a mirror is curved in this way, it is called concave , and the nature of this curve changes the situation dramatically.
Focal point
The light beams reflect off the curved surface so that they are directed to the same point. It turns out that any light beam traveling towards the mirror and parallel to the black line in the figure will be reflected so that it will pass through this poin
Optical axis
Physicists call the black line in the figure the optical axis of the mirror.
Equation
The more curved the mirror, the closer the focal point will be to that mirror. In fact, a very simple equation relates the focal point to the radius of curvature of a spherical mirror:
Parabola
It is important that you understand exactly how these mirrors are curved. For a curved mirror to focus all horizontal light beams to a single focal point, the mirror must be shaped as a parabola
Spherical aberration
The closer light from the object strikes the outer edges of the mirror, the more noticeable the distortions are. This effect is called spherical aberration , and it is the result of the fact that a spherical mirror only approximates a parabolic mirror.
Important facts
1. When a beam of light travels horizontally and hits a spherical, concave mirror, it is reflected so that it passes through the mirror's focal point.
2.
When a beam of light travels through the focal point of a spherical, concave mirror, it is reflected so that it travels horizontally.
3.
When a beam of light travels through a spherical, concave mirror's radius of curvature, it will be reflected backwards along precisely the same path.
Ray Tracing
This kind of exercise is called ray tracing. Light beams are often called light rays, and since this exercise traced where these light rays travel, we call it ray tracing
Real image
An image formed as the result of intersecting light beams
Opaque
A wall is considered an opaque (oh payk') object, which means light cannot travel through it.
Transparent
Light can also run into a transparent (or semi-transparent) object. Transparent objects allow light to pass through them.
Refraction
The process by which a light ray bends when it encounters a new medium
Index of refraction
The ratio of the speed of light in a vacuum to its speed in another medium
Refraction of air
The index of refraction of air (to three significant figures) is 1.00.
Dispersion
Everyone knows that if you shine white light through a prism at the proper angle, the light will separate into the colors of the rainbow. In fact, water droplets suspended in the sky can act as tiny prisms, turning sunlight into a rainbow. This is called
Light rays
1. All light rays that enter the lens traveling horizontally will exit the lens traveling through the focal point.
2.
All light rays that enter the lens traveling through the focal point will exit the lens horizontally.
3.
All light rays that enter the lens traveling directly towards the center will experience no deflection as they exit the lens.
Diverging lens
Another basic type of lens used in optics is the diverging lens. Like a converging lens, this lens uses the fact that light bends when it encounters glass. Also, like a converging lens, it is made of curves that are arcs of a sphere. However, unlike a con
Myopia
If a person has myopia , the combination of the lens and cornea focuses light too strongly.
Hyperopia
If a person has hyperopia, the cornea and lens cannot bend light strongly enough and, as a result, the image is formed behind the retina.
Definition of Momentum
When an object is in motion, it has momentum. Momentum is a vector quantity, and its definition is best expressed mathematically:
Momentum
In order to get momentum, we take mass (the SI unit is kg) and multiply by velocity (the SI unit is ). The resulting SI unit is . Unlike many of the other complicated units in physics, this does not have an abbreviation or another name. It is just a . I d
Impulse
Since the change in an object's momentum is a rather fundamental quantity to examine when studying motion, physicists often rearrange Equation (9.6) to solve for it:
Impulsive forces
The concept of impulse is most useful when you deal with forces that are applied over a short time interval. These forces are often called "impulsive forces" to emphasize the fact that impulse plays a critical role.
Impulse 2
Since the board delivered the impulse over a short time interval, the force it applied was large. After all, since impulse is defined as F �?t, if ?t is small, F must be large. In the case of the bed sheet, however, the time interval (?t) was larger, so i
Law of Momentum Conservation
When the sum of the forces working on a system is zero, the total momentum in the system cannot change.
Kinetic energy
Think about it. Before the collision, the kinetic energy of the system was:
Recoil velocity
The velocity that an object develops in response to launching another object, which is a result of the Law of Momentum Conservation
Angular momentum
When an object moves on a circular path, it is more informative to study its angular momentum than to study its linear momentum.
Angular velocity
The rate at which the position angle of an object changes in rotational motion
Radius
In the same way, the angular momentum of an object traveling in a circle is equal to the linear momentum (m�v) times the radius of the circle:
Law of Angular Momentum Conservation
If the sum of the torques on a system is equal to zero, the angular momentum never changes.
Periodic motion
Motion that repeats itself regularly
Hooke's Law
Hooke coined the term "cell." In this module, however, we won't concentrate on his impressive accomplishments in the field of biology. Instead, we need to look at a law that he developed when he studied the behavior of springs.
Displacement
Experiments such as the one that you just performed led Robert Hooke to determine this rather simple equation for the relationship between the force applied by a spring (F) and the displacement through which it stretches (?x):
Equilibrium position
The position of an object when there are no net forces acting on it
Restoring force
A force, directed towards the system's equilibrium position, which is applied as a result of the system's displacement from equilibrium
Spring constant
Now, if you're a little confused at this point, don't worry. A concrete example should clear everything up. Before we do that, however, we need to talk about the spring constant , which is given by "k" in Equation (10.1). First (as usual), we need to worr
Lines
you graphed the force versus the distance that the spring stretched. If you recall from algebra, the equation of a line is:
Amplitude
The maximum distance away from equilibrium that an object in periodic motion travels
Simple harmonic motion
Periodic motion whose period is independent of its amplitude
Major aspects
� In a mass / spring system, the maximum acceleration occurs at each amplitude of the motion.
� In a mass / spring system, the maximum speed occurs at the equilibrium position.
� In a mass / spring system, the acceleration is zero at the equilibrium posit
Equations
As a result, Equation (10.6), which we derived a while ago, applies to the mass / spring system, as long as we make an adjustment to one of the variables. Let's look at that equation again:
Equation
In addition, since the object is not moving in a circle, its acceleration is not centripetal anymore. As a result, I will drop the "c" in "ac.
Equation
This also allows me to get rid of the negative sign, since it denotes direction. Thus, the scalar equivalent of Equation (10.1) is:
Equation
Also, let's suppose I want to analyze the object when it has moved all the way out to the amplitude of its motion. In that case, ?x = A. I will make that substitution as well:
Equation
Now we can take this equation and solve for acceleration:
Equation
Finally, we can rearrange this equation to solve for the period (T). Notice that the amplitude drops out because it exists in the numerator on each side of the equation. After rearranging, we get the following equation:
Equation
Thus, even though I don't expect you to understand the derivation of Equation (10.11), I do expect you to remember these two critical things:
Motion
This graph, then, shows us a couple of things about the motion of a mass / spring system that we need to remember:
Equation
Although the derivation is a bit too long for this course, the equation itself is very straightforward:
Radians
First, remember that there are two units with which I can measure an angle. The typical unit is degrees, but often in mathematics we use the unit of radians to measure an angle.
Important facts
When the angle of displacement for a simple pendulum is small (less than about 20�),the pendulum exhibits simple harmonic motion.
Two men run down a road. They each run at the same velocity, but the first has more momentum than the second. How is that possible?
The first one has a greater mass.
A physics teacher tells you that she observed two objects of equal mass traveling with identical speeds. She claims that their momenta were different, however. How is that possible?
They have different velocity directions
Explain (in terms of the concepts we have learned in this module) how air bags reduce injuries in traffic accidents.
The airbag absorbs the impact of the deceleration and increases the deceleration rate and distance, so the person does not experience as much force.
When a balloon is blown up and then released, it flies about as the air escapes. Why?
The molecules come together to escape, the molecules have momentum.
Which of the following are legitimate units for angular momentum?
Angular momentum must have mass unit times distance times velocity.
Can a cat with no tail always land on its feet when it falls? Why or why not?
No, you see, before the cat starts to move its tail, it is experiencing no rotational motion. As a result, its angular momentum is zero. When the cat begins to move its tail in a circle, however, the tail suddenly has angular momentum. In order for the an
A 125-gram toy car travels with a velocity of 5.4 m/sec at 300�. What is its momentum?
It's momentum would be MVR= -0.68 kg at 300 degrees
A 365-kg car traveling horizontally at 21.1 m/sec slams into a tree and comes to a halt in 0.22 seconds. What force did the tree exert on the car in order to stop it?
A force of F=m
a=-3.5
10^4 Newtons traveling horizontally is required to have stopped the car.
A 250.0-gram baseball is thrown horizontally to a batter at 38 m/sec. The batter hits the ball and sends a line drive horizontally at -52 m/sec. If the bat delivered a force of -201 Newtons, how long were the ball and bat in contact?
The momentum of the ball was traveling 52 m/sec horizontally when it stopped once it came in contact with the bat. The ball and bat were in contact for 0.11 seconds which represents the impulse
A 2.34-kg gun has a recoil velocity of 5.2 m/sec. At what velocity does it fire its 95-gram bullets?
The bullets will fire at a momentum and velocity of 130 m/s opposite of the recoil velocity.
A 60.0-kg ice skater stands motionless and catches an 8.0-kg medicine ball (a heavy ball used in athletic training and physical therapy) that was traveling towards her horizontally at 3.7 m/sec. What will her velocity be after she catches the ball?
Her velocity after she catches the ball will be 0.44 m/s
A 975-kg train car coasts slowly (v = 3.1 m/sec) under a hopper that fills it with coal. If the car's velocity slows to 1.2 m/sec, what mass of coal was loaded into it?
1.5*10^3 kg of coal was loaded into the car.
The moon has a mass of 7.36 x 10^22 kg and orbits the earth with a linear speed of 1.00 x 10^3 m/sec and an orbital radius of 3.8 x 10^8 m. What is the moon's angular momentum?
2.8*10^34
A child twirls a toy plane on a string. He twirls it so that its radius of motion is 45 cm and its speed is 3.9 m/sec. Without adding any torque, he lets out more string so that the radius of motion increases to 98 cm. What is the plane's new speed?
1.8 m/s
A mass / spring system is pulled 5.4 cm from equilibrium and then released. Its period of motion is measured to be 1.1 seconds. The system is then brought to a halt. Next, it is displaced 10.0 cm from its equilibrium position and released again. What will
1.1 seconds
In a mass / spring system, where does the mass have the greatest amount of kinetic energy?
At the equilibrium point of its motion, a mass / spring system has no potential energy and its maximum kinetic energy (and therefore its maximum speed).
In a mass / spring system, where does the mass experience the greatest acceleration?
In a mass/spring system, the mass experiences the greatest acceleration at the amplitude.
Keeping in mind that you are trying to study simple harmonic motion, should you displace the pendulum a large or small distance from equilibrium?
A small distance, because you are only trying to find a simple harmonic motion whose period is independent of the amplitude.
You construct two pendulums. The first has twice the mass as the second. Otherwise, they are identical. How do the periods of the pendulums compare?
They will be the same, because their mass will not affect the period of pendulum.
You construct two pendulums. The first is significantly shorter than the second. Otherwise, they are identical. How do the periods of the pendulums compare?
The second one will have a longer period than the first.
If the motion of a mass / spring system has an amplitude of 12.1 cm, how far from equilibrium was it initially displaced?
12.1 cm, because that is the maximum distance from the equilibrium it can be.
A 34.5 kg mass bounces on a spring (k = 12.1 Newtons/m). What is the period of its motion?
10.6 seconds
An object is hung on a spring, causing the spring to stretch 15.1 cm. If the force constant of the spring is 2.9 Newtons/meter, what is the mass of the object?
0.045
A 5.61-kg fish is hung on a spring scale. The spring stretches 9.2 cm in response. The fisherman, in an effort to make the fish seem heavier, pulls down on the fish, displacing it an additional 3.1 cm. His wife, trying to make him honest, slaps his hand,
0.61
What is the total energy of the mass / spring system?
0.230 Joules
What is the mass's maximum speed?
0.101 m/s
What will its speed be when it is 10.0 cm from equilibrium?
0.0952 m/s
An astronaut has lost her star charts and has no idea what planet she has just landed on. Although she has no star charts, she does have a list of all known planets and their gravitational accelerations. Being a good physicist, she puts together a 0.75-m
Mars
A wave oscillates in the horizontal dimension and propagates in the vertical dimension. Is it a longitudinal or a transverse wave?
Transverse
Substance A is more dense than substance B. In which substance does light most likely travel faster?
Substance B
Given substances A and B above, if A is a solid and B is a liquid, in which does sound travel faster?
Substance A
A soprano sings with a very high pitch while a tenor sings with a lower pitch. Which singer's sound waves have the larger wavelength?
The Tenor
Two singers sing at exactly the same pitch, but the first is louder than the second. What is the difference between the two singers' sound waves?
The first one will be higher than the second one.
What is the wavelength of light if its frequency is 1.2 x 103 Hz?
250000 m
What is the frequency of a sound wave traveling in 25 oC air if its wavelength is 0.512 m?
678 Hz
What is the temperature if a 612.0-Hz sound wave has a wavelength of 0.5800 m?
38.8 degrees Celsius
If the temperature during a thunderstorm is 11 oC and the thunderclap is heard 2.9 seconds after the lightning flash is observed, how far away from the observer was the lightning?
980
A siren emits a sound wave with a frequency of 440 Hz when it is stationary. If you are stationary and hear the siren with a frequency of 555 Hz, is the siren moving toward you or away from you?
The siren is moving closer
Two metals are studied. Metal "A" has a lower work function than metal "B." In the study, light of decreasing frequency is shone on each metal, and the minimum frequency required to liberate electrons from the metal is measured. Which metal has the highes
Metal B
A car's horn has a frequency of 278 Hz when it is stationary. If the car is moving away from you with a speed of 25.6 m/sec and the driver blows the horn, what frequency do you hear? (Assume the speed of sound is 347.0 m/sec in this situation.)
259 Hz
A stationary siren blows with a constant frequency of 551 Hz. You begin riding your bike towards the siren at 10.0 m/sec. What frequency do you hear? (Assume the speed of sound is 347.0 m/sec in this situation.)
567 Hz
The work function of copper is 4.94 eV. What is the lowest frequency of light that will result in electrons being liberated from the metal?
1.19*10^15 1/sec
Light of wavelength 211 nm is shone on gold, which has a work function of 5.31 eV. What is the maximum kinetic energy of the electrons that are emitted from the metal?
0.5 eV
What kind of images are formed in a flat mirror: real or virtual?
Virtual
What is the difference between a real image and a virtual image?
Virtual image - An image formed as the result of extrapolating light beams
If substance A has half the index of refraction of substance B, which is (most likely) more dense?
Substance B
State the Law of Reflection.
The angle of reflection equals the angle of incidence.
If you want to avoid spherical aberrations in your curved mirrors, what kind of mirror should you use?
A parabolic mirror
You are looking at an object up close. Suddenly, you look at an image far away. What happens in your eye to change its focus?
The ciliary muscles contract to adjust to the distance change, so the eye changes the shape of its lens.
In the situation described above, what would you do to change the focus of a camera?
The camera changes the position of the lens.
An object is placed 7.0 cm away from a concave spherical mirror whose radius of curvature is 10.0 cm. Draw a ray tracing diagram to illustrate what the image will look like. Is it real or virtual? Is it upright or inverted? Is the image magnified, reduced
Real image
An object is placed 2.5 cm away from a spherical, convex mirror whose radius of curvature is 3.0 cm. Draw a ray-tracing diagram to illustrate the image, and determine whether the image is real or virtual, upright or inverted, and magnified or reduced.
Virtual image
Light traveling in ice (n = 1.31) is incident on air at an angle of 35�. What is the angle of refraction?
49 degrees
The speed of light in a certain plastic is 2.4 x 108 m/sec. What is the index of refraction of the plastic?
1..3
refracts at 56.3�, what is the index of refraction of diamond?
2.42
A converging lens has a focal point that is 6.0 cm from its center. If an observer looks through the lens at an object 1.5 cm from the lens, what will the image look like? Is it real or virtual? Is it upright or inverted? Is the image magnified, reduced,
Virtual image
A converging lens has focal points that are 4.0 cm from its center. If an observer looks through the lens at an object 6.0 cm from the lens, how does the image appear? Is it real or virtual? Is it upright or inverted? Is the image magnified, reduced, or e
Real image
A diverging lens has focal points that are 16.0 cm from its center. If an observer looks through the lens at an object 10.0 cm from the lens, how does the image appear? Is it real or virtual? Is it upright or inverted? Is the image magnified, reduced, or
Virtual image