Simple Harmonic
Motion, Waves, and
Sound
Mr Veach
Pearland ISD Physics
Simple Harmonic Motion
Periodic motion- a motion that is repeated
with some set frequency.
 Simple Harmonic Motion - a type of
periodic motion where the restoring force is
directly proportional to the displacement
and acts in the direction opposite to that of
displacement
 Two common types of simple harmonic
motion



vibrating spring/mass system
oscillating pendulum.
Examples of SHM?
Oscillating Spring/Mass Systems

A Mass Springs System will vibrate
horizontally (on a frictionless
surface) or vertically.
Oscillating Spring/mass
Systems
Damping
In an ideal system, the mass-spring
system would oscillate indefinitely.
 Damping occurs when friction slows
the motion.



Damping causes the system to come to
rest after a period of time.
If we observe the system over a short
period of time, damping is minimal,
and we can treat the system like it is
ideal.
Simple Pendulum

Simple pendulum – consists of a mass
(called a bob) that is attached to a fixed
string
Simple Pendulum
At maximum displacement from equilibrium,
a pendulum bob has maximum potential
energy; at equilibrium, this PE has been
converted to KE.
 The total mechanical energy
will remain constant.

Describing Simple Harmonic
Motion
Amplitude – the maximum displacement
from equilibrium.
 Period (T) – the time to execute one
complete cycle of motion; units are
seconds.
 Frequency (f) – the number of complete
cycles of motion that occur in one second;
units are cycles per 1 second, or s-1 (also
called Hertz).

Describing Simple Harmonic
Motion

Frequency is the reciprocal of period,
so
Sample problems
A string vibrates at a frequency of 20 Hz. What is
its period?
You want to describe the harmonic motion of a
swing. You find out that it take 2 seconds for the
swing to complete one cycle. What is the swing’s
period and frequency?
Waves

A wave is the motion of a disturbance of
some physical quantity.

A wave transfers energy without a largescale transfer of matter.
Types of waves
Mechanical vs. non-mechanical
 Pulse vs. periodic
 Transverse vs. longitudinal

Types of waves:
Mechanical and Nonmechanical

Mechanical Waves


Require a Medium
Examples


Sound Waves, Water Waves, Shock Waves from an
explosion
Non-mechanical Waves


Do not require a medium
Examples

Electromagnetic Waves (Light, X-rays, Radio Waves)
Types of Waves
Pulse and Periodic Waves

Pulse Wave


A wave which consists of a single non-repeated
disturbance or pulse
Periodic Wave

A wave whose source is some form of periodic
motion.
Transverse Waves

Transverse Wave

A wave whose particles vibrate perpendicular
to the direction of the travel of the wave

Examples



Surface waves on water
Electromagnetic waves
Guitar string
Transverse Wave
Waveform diagram

The shape of a transverse wave can be
described using a waveform diagram


This diagram allows us to see crests and
troughs
It also allows us to measure wavelength and
amplitude
Longitudinal Waves

Longitudinal Waves

A wave whose particles vibrate parallel to the
direction of travel of the wave

Examples

Sound waves, Compression waves in an explosion, P
waves from an earthquake.
Longitudinal Waves
Longitudinal Waves
are sometimes
referred to as
density waves
 They can be
represented by the
same waveforms
as transverse
waves.

Compression
Characteristics of Waves:
Frequency and Period

Frequency (f) - the number of waves passing a
reference point per second.



Period (T) – the time between the passage of two
successive wave crests (or troughs) past a
reference point.


Frequency is measure in cycles/second
1 Cycle/second = 1 s-1 = 1 Hertz
The period is a time interval, so it is measured in
seconds.
The frequency is the reciprocal of the period.

We also say frequency and period are inversely
proportional.
T
= 1/f
f = 1/T
Characteristics of Waves:
Wavelength

wavelength (λ) – distance between two
adjacent similar points of the wave, such
as from crest to crest or trough to trough
Characteristics of Waves:
Wave Speed
Wave Speed: The speed of the moving
disturbance
 Relationship between frequency, speed,
and wavelength:


v = f λ, where



v = wave speed (m/s)
f = Frequency (Hertz) or (s-1)
λ = wavelength (m)
Problem

A tuning fork produces a sound with a
frequency of 256 Hz and a wavelength in
air of 1.35 meters.

What is the speed of sound in air?




f = 256 Hz and ʎ = 1.35m
v = 256Hz • 1.35m
v = 345.6 m/s
What is the period of this tuning fork?



f = 256 Hz,
T= 1/f
T=1/256 = 0.004s
Characteristics of Waves:
Amplitude

Amplitude – the maximum displacement
of the vibrating particles of the medium
from their equilibrium positions.

The amplitude of a wave is related to the
energy transported by the wave.
Interactions of Waves

Two Types of Interactions



Constructive Interference
Destructive Interference
Superposition – the combination of two
overlapping waves.

When waves overlap, the amplitudes of the
waves at each point are added to find the
resultant displacement.
Wave Interference
Constructive Interference

Constructive Interference – when
individual waves on the same side of the
equilibrium position are added together to
form the resultant wave.

The resultant displacement is larger than
either of the component displacements
Interactions of Waves
Constructive Interference Cont
Interactions of Waves
Constructive Interference Cont
Interactions of Waves
Constructive Interference
Interactions of Waves
Constructive Interference gone bad
Destructive Interference

Destructive Interference – when individual
waves on opposite sides of the equilibrium
position are added together to form the
resultant wave.

The resultant is smaller than either of the
component displacements.
Interactions of Waves
Destructive Interference
Interactions of Waves
Destructive Interference
Interactions of Waves
Destructive Interference
Interactions of Waves
Standing Waves

standing wave – a wave pattern that results when
two waves of the same frequency, wavelength, and
amplitude travel in opposite directions and interfere.
Interactions of Waves
Standing Waves

node – a point in a standing wave
that always undergoes complete
destructive interference and
therefore is stationary.

anti-node – a point in a standing
wave, halfway between two nodes,
at which the largest amplitude
occurs.
Sound Waves
Sound Waves are longitudinal waves.
 Sound waves are mechanical waves, which
means they must travel through a medium.




Air and water are common mediums that sound
travels through
Sound does not travel in space or in a vacuum.
Sound waves spread out in three dimensions.

This is why we can hear around corners
Frequency of sound waves


The frequency of a sound wave is related to
its pitch
Higher the frequency the higher the pitch

pitch is a measure of frequency

High Frequency
High Pitch
Low Frequency
Low Pitch
Frequency and Wavelengths of
Sample Sound Waves

880 Hz

2200 Hz
W ave Sound
W ave Sound
W ave Sound

20 Hz

80 Hz

160 Hz

4400 Hz

220 Hz

8800 Hz

440 Hz

13200 Hz
W ave Sound
λ = 17 m
W ave Sound
W ave Sound
W ave Sound
W ave Sound
W ave Sound
W ave Sound
λ = .77 m

22000 Hz
W ave Sound
λ = .04 m
The Speed of Sound

Sound travels more slowly than light

Think about thunder and lightning: what do you
observe first?
The Speed of Sound
The speed of sound depends on the medium.
 Sound waves can travel through solids, liquids,
and gasses.
 The speed of sound in a given medium depends
on how quickly one particle can transfer its
motion (kinetic energy) to another

The Speed of Sound
The more rigid the medium, the faster sound
travels through it.
 Sound travels faster in solids.
 faster in water than in the air
 faster in glass compared to water
 The temperature of the medium may also
affect the speed of sound.

The Doppler Effect
 An
apparent shift in frequency for a
wave due to relative motion between the
source of the wave and the observer.
 The
Doppler effect can be observed for
any type of wave - water wave, sound
wave, light wave, etc.
 We
are most familiar with the Doppler
effect because of our experiences with
sound waves.
The Doppler Effect
Recall an instance when a police car or
emergency vehicle was traveling towards you
on the highway.
 As the vehicle approached with its siren
blasting, How did the pitch of the siren
change as the car passed by?

The Doppler Effect
The Doppler Effect

Approaching you the pitch was high; and then
suddenly as the vehicle passed by, the pitch
of the siren sound was lower.
The Doppler Effect
When the sound is moving toward you: The
motion results in more wave crests reaching
the observer per second, therefore, apparent
frequency is increased.
 When the sound is moving away from you: the
relative motion results in fewer wave crests
reaching the observer per second, so the
apparent frequency is decreased.
 It is important to note that the Doppler
effect does not result in an actual change in
the frequency of the sound from the source.

The Doppler Effect
Breaking the “Sound Barrier”
Breaking the “Sound Barrier”
The Doppler Effect