simple harmonic motion, waves, and sound harmonic motion, waves, and sound mr veach pearland isd...

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


Wavelength

wavelength (λ) – distance between two adjacent similar points of the wave, such as from crest to crest or trough to trough


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


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

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ch14_4_movanim.swf


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


Constructive Interference Cont


Constructive Interference gone bad


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.


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.


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”

The Doppler Effect

simple harmonic motion, waves, and sound harmonic motion, waves, and sound mr veach pearland isd...

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