T = 2 ·  ·
L g
PHYSICS STUDY GUIDE
CHAPTER 15: WAVES
1. SIMPLE HARMONIC MOTION
Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium.
A simple pendulum consists of a mass called a bob, which is attached to a fixed string.
Period of a simple pendulum:
T = Period
L = Length of the string
G = gravitational constant
(seconds)
(meters)
(m/s 2 )
A mass-spring system consists of a mass hanging at the bottom of a spring.
Period of a mass-spring system:
T = 2 ·  · m k
T = Period m = mass k = Spring constant
(seconds)
(kilograms)
(N/m)
2. WAVES
 Waves are disturbances that travel in time.
 Waves are created by a vibrating source.
 Waves are created in a sinusoidal shape.
DEFINITIONS
 Medium : A physical environment through which a disturbance can travel.
 Transverse wave : A wave whose particles vibrate perpendicularly to the direction the wave is traveling.
 Longitudinal wave : A wave whose particles vibrate parallel to the direction the wave is traveling.
 Mechanical wave : A wave that requires a medium through which to travel.
 Electromagnetic wave : A wave that DOES NOT require a medium through which to travel.
 Crest : The highest point above the equilibrium position.
 Trough : The lowest point below the equilibrium position.
 Compression: Section of a longitudinal wave of high density.
 Rerefaction : Section of a longitudinal wave of low density.

3. PHYSICAL QUANTITIES
PHYSICAL
QUANTITY
Amplitude
DEFINITION
Maximum displacement from equilibrium position.
Period Time for one cycle.
SYMBOL
A
T
UNITS meters
(m) seconds
(s)
DEPENDS
ON
Vibrating source
Vibrating source
Frequency Amount of cycles in one second.
f
Hertz
(Hz)
Vibrating source
Wavelength
Wave speed
Length of one cycle. The distance between two adjacent similar points of a wave, such as from crest to crest or from trough to trough (position graph).
Speed at which one disturbance propagates.
 v meters
(m)
(m/s)
Medium
Vibrating source &
Medium
4. REPRESENTATION OF WAVES
MECHANICAL WAVES
Waves are represented in position and waves are represented in time.
Representation of position of a mechanical transverse wave
Representation of time of a mechanical transverse wave one cycle measures the WAVELENGTH one cycle measures the PERIOD
LONGITUDINAL WAVES
Waves are represented in position and waves are represented in time.

Representation of position of a mechanical longitudinal wave
Representation of time of a mechanical longitudinal wave one cycle measures the WAVELENGTH
5. MATHEMATICAL MODELS one cycle measures the PERIOD
PERIOD VS. FREQUENCY : They are the inverse of each other.
 Period: Time for one cycle T =
1 f
 Frequency: Amount of cycles in one second f =
1
T
WAVE SPEED : Speed at which one disturbance propagates.
 Speed: Distance traveled (  ) over time traveled (t) v =

T
or v =  · f v T v f
6. PROPERTIES OF WAVES
 INTERFERENCE (SUPERPOSITION)
Constructive Interference:
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave.
Destructive Interference:
A superposition of two or more waves in which individual displacements in opposite sides of the equilibrium position are added together to form the resultant wave.

 REFLECTION
When a pulse travels down a rope whose end is free to slide up the post, the pulse is reflected from the free end.
When a pulse travels down a rope that is fixed at one end, the reflected pulse is inverted
7. STANDING WAVE
 Standing Wave : A wave pattern that results of multiple superposition and reflections. Waves have the same frequency, wavelength and Amplitude.
 Node : A point in a standing wave that maintains the minimum or NO amplitude.
 Antinode : A point in a standing wave halfway between two nodes, at which the larder displacement occurs.
 Fundamental Frequency : The lowest frequency of vibration of a standing wave.
 Harmonic Series: A series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency (n = 1, 2, 3, 4, . . . )
Standing wave on a string or in an open pipe
Fundamental Frequency f
1
=
( 2 v
· L )
Frequency of any harmonic f n
= n ·
( 2 v
· L )
(n = 1, 2, 3, 4, . . .