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 large-scale 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.
Frequency is measure in cycles/second
1 Cycle/second = 1 s-1 = 1 Hertz
Period (T) – the time between the passage of two successive wave crests (or troughs) past a reference point.
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.
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 Low FrequencyHigh Pitch Low Pitch
Frequency and Wavelengths of
Sample Sound Waves 20 Hz
80 Hz
160 Hz
220 Hz
440 Hz
880 Hz
2200 Hz
4400 Hz
8800 Hz
13200 Hz
22000 HzWave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
λ = 17 m
λ = .04 m
λ = .77 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.
When the sound is moving toward you: The motion results in more wave crests reaching the observer per second, therefore, apparentfrequency 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
The Doppler Effect
Breaking the “Sound Barrier”
Breaking the “Sound Barrier”
The Doppler Effect