Chapter 25 – Vibrations and Waves
A wiggle in time is called a vibration, we call vibrations wiggles in time because they cannot happen in
one instant but need time to move back and forth.
• A wiggle in space and time is called a wave, we it this because it cannot happen in one instant because it
needs time to move, but it also cannot happen in just one space because it needs space to move.
25.1 – Vibration of a pendulum
• A pendulum is a weight suspended at the end of a string that can swing back and forth.
o Pendulums can be used as time keeping device in a clock.
o The time of the back and forth movement is called a period
The period depends only on the length of the string and the acceleration of gravity. The
longer the string, the longer the period.
25.2 – Wave description
• The back and forth motion of a pendulum is called simple harmonic motion.
o If you suspend a pendulum filled with sand over a stationary piece of paper you will see a
straight line form under it as it goes back and forth.
o If you suspend a pendulum filled with sand over a moving sheet of paper a curved line begin to
form. If the paper is moving at a constant speed the curve that you see is called a sine curve.
• Another example of simple harmonic motion is seen with a spring that has a weight attached to it as it
goes up and down.
o If you attached a marker to the side of the weight you would see similar effects as you did with
the sand in the pendulum.
• The high point of a wave is called a crest, and the low point of a wave is called a trough
o If you find the midpoint between the crest and the trough of a wave, then the distance from that
line to the crest or the trough is the amplitude of that wave.
• The wavelength of a wave is the distance from the top of one crest to the top of the next (it could also
be measured from the bottom of one trough to the bottom of the next).
• The frequency is how often a vibration occurs. This means the number of back and forth vibrations it
makes in a given time (usually a second). A complete back and forth is one cycle, and if that took one
second then the frequency would be one cycle per second.
o We measure frequency in hertz (Hz). One cycle per second is one hertz.
AM radio waves are in KHz (1,000 Hz), and FM radio waves are in MHz (1,000,000 Hz)
• The source of all waves is a vibrating object, and the frequency of that vibrating source and frequency of
the wave are the same (the antenna on a radio tower is vibrating at the frequency of the station).
• Frequency and period are related by the following equation:
o Frequency = 1/Period
o Period = 1/Frequency
25.3 Wave motion
• Sound is energy traveling in waves as are radio and television signals
• When energy travels in wave form it is able to affect far away objects without any transfer of energy
directly between the two objects.
• When sound moves through air, the sound wave is actually creating a disturbance in the air molecules.
25.4 Wave Speed
• The speed of a wave depends on the medium it moves through. The equation for wave speed is:
o Wave speed = wavelength x frequency
v = λf
Wavelength and frequency vary inversely to produce the same wave speed for all sounds
(see table 25.1 on page 377)
25.5 Transverse Waves
• Whenever the motion of the medium (air, or water, or rope, or whatever the wave is moving through) is
perpendicular to the direction the wave is traveling, then the wave is a transverse wave.
o String instruments and the surface of water both produce transverse waves.
•
25.6 Longitudinal Waves
• When the particles of the medium move back and forth in the same direction that the wave is moving (as
in not at right angles) then the wave is a longitudinal wave.
• You may use the figure 25.9 on page 379 of your book to visualize the difference between a transverse
and a longitudinal wave. You also will see these in the slinky snaky lab.
25.7 Interference
• Two waves can exist in the same space, and when that happens they influence each other. We call this
influence an interference pattern.
o Constructive interference is when two waves affect each other in a positive way and produce a
single wave of greater amplitude. In other words they add together.
o Destructive interference is when the two waves affect each other in a negative way and cancel
each other out.
o When two waves combine constructively way we say that they are in phase with each other.
o When two waves combine destructively, we say that they are out of phase with each other.
25.8 Standing Waves
• A rope tied to the wall and shaken just right will produce a standing wave which is when the wave
going out and the wave coming back work together so that the nodes (which are specific points along
the wave) don’t move at all. When a standing wave is viewed from the side, you can identify the shape
of the waves and the nodes very well. There are drawings of standing waves on page 381 of your book).
o The point halfway between two nodes is called an antinode, and the anti node is the top of the
crest or the bottom of the trough of the wave.
o The reason these nodes occur is that you have a wave going out from you to the wall and a wave
coming back from the wall to you. These waves are not in phase with each other, and the nodes
are the points where they are totally out of phase and are canceling each other out completely.
25.9 The Doppler Effect
• The Doppler Effect is the apparent change in frequency due to the motion of the source (or in some
cases of the receiver). The simple example the book gives of the bug stationary on the water and the
bug moving across the water is illustrated on page 382.
o The Doppler Effect is what is responsible for many things we experience in our daily lives, like
the changing pitch of the car horn as it drives past you.
o The Doppler Effect is also used in police radar by comparing the frequency of the radar being
emitted by the car, and the frequency of the reflected waves coming back from the car.
o The Doppler Effect also happens with light. We call the increase in frequency a blue shift
because it moves toward the blue end of the spectrum. We call the decrease in frequency a red
shift because it moves toward the red end of the spectrum.
25.10 Bow Waves
• A bow wave is created by an object moving faster than the waves that it creates and it is a pattern made
by over lapping crests that make a V shape.
• We used to think that we couldn’t “break the sound barrier,” but it’s like a boat on a lake. If the boat
travels faster than the waves it creates, then it always enters smooth water. It is the same for the plane
that goes faster than sound, it outruns the sound waves that it creates, and always flies into smooth air.
25.11 Shock Waves
• Just like a boat traveling in water creates a 2-D bow wave, a plane traveling faster than the speed of
sound (supersonic) creates a three dimensional shock wave. The shock wave is created by overlapping
spheres of sound waves, and creates a conical shape. This shape extends all the way until its edge hits
the earth. When this happens, any listeners on the ground below hear a large crack called a sonic boom.
We can compare hearing this sonic boom to being hit with the crest of a speedboats bow wave.
o The sound of the sonic boom will be heard by each person the plane passes over, not just the
moment when the plane first reaches the speed of sound (a common misconception).
o A plane doesn’t need to be actually making noise to make a sonic boom.
o We hear baby sonic booms when we crack a whip, release a supersonic bullet, or snap a towel.