Sound

Longitudinal waves

Producing a Sound Wave

· Sound waves are longitudinal waves traveling through a medium

· A tuning fork can be used as an example of producing a sound wave

Using a Tuning Fork to Produce a Sound Wave

· A tuning fork will produce a pure musical note

· As the tines vibrate, they disturb the air near them

· As the tine swings to the right, it forces the air molecules near it closer together

· This produces a high density area in the air· This is an area of compression

Using a Tuning Fork, cont.

· As the tine moves toward the left, the air molecules to the right of the tine spread out

· This produces an area of low density· This area is called a

rarefaction

Using a Tuning Fork, final

· As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork

· A sinusoidal curve can be used to represent the longitudinal wave· Crests correspond to compressions and troughs to rarefactions

Sound Waves and Sound

· Frequency determines pitch

· Amplitude determines volume

· A sound wave must be within a certain frequency range and above a certain minimum amplitude for us to hear it.

Categories of Sound Waves

· Audible waves· Lay within the normal range of hearing of the human

ear· Normally between 20 Hz to 20,000 Hz· Notice: this range is based on FREQUENCY.

· Infrasonic waves· Frequencies are below the audible range· Earthquakes are an example

· Ultrasonic waves· Frequencies are above the audible range· Dog whistles are an example

Range of Human Hearing

· Humans, on average, can detect tones from 20Hz to 20,000 Hz.

· This range gets smaller with age. As you get older, you loose the ability to hear the high end of the range.

· Different animals have different ranges of hearing. Cool graphic

Decibel Scale

· Sound volume is commonly measured in decibels.

· The decibel system is calibrated to human hearing; thus, the lowest level of sound (at a frequency of 1,000 Hz) that a theoretical human can detect is the zero set point for the scale. This is called the “threshold of hearing.”

Threshold of hearing

· The average person can detect a 1000 Hz sound at a minimum of 4 decibels, but this changes with the frequency being heard.

· This graph shows the minimum sound volume the average person can detect based on the frequency of sound

Threshold of Pain

· The loudest sound an average person can tolerate is 120 – 130 decibels.

· The decibel system is logarithmic; this means that each step on the scale is a factor of 10x greater than the one before.

· So, 130 dB is not 130 times greater than 1 dB, but is 1 x 1013 times greater!

Hearing Safety

· Hearing damage can result from exposure to loud sounds.

· Studies of rock musicians and animal studies have suggested that exposure to unsafe levels of sound can lead to temporary or permanent hearing impairment, such as

· Tinnitus (ringing in the ears) to hearing loss.

Sound Effects

Changes in Frequency

Doppler Effect

· A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer.· When the source and the observer are moving

toward each other, the observer hears a higher frequency

· When the source and the observer are moving away from each other, the observer hears a lower frequency

Doppler Effect, cont.

· Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves

· Assumptions:· The air is stationary· All speed measurements are made relative to

the stationary medium

Doppler Effect, Case 1 (Observer Toward Source)

· An observer is moving toward a stationary source

· Due to his movement, the observer detects more wave fronts per second

· The frequency heard is higher than the one produced

Doppler Effect, Case 1(Observer Away from Source)

· An observer is moving away from a stationary source

· The observer detects fewer wave fronts per second

· The frequency appears lower

Doppler Effect, Case 1 – a moving observer

· When the observer is moving and the source is stationary, the observed frequency is

· When moving away from the stationary source, use –vo; when moving toward the stationary source, use + vo;

±

IB parlance, moving observer

· The observed frequency is written

as f’· The emitted

frequency is written

as f

· The observer’s velocity is written as

uo

f’ = f [ (v ± uo) ÷ v]

±

Doppler Effect, Case 2 - a Moving Source

· As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases

· As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower

Doppler Effect Equation, Moving Source

· Use –vs when the source is moving toward the observer and +vs when the source is moving away from the observer

±

In IB parlance,

· The observed frequency is written as f’

· The emitted frequency is written as f

· The observer’s velocity is written as us

f’ = f [v / (v ±us)]

±

Doppler Effect, General Case

· Both the source and the observer could be moving

· When moving towards, vo is a postive value and vs is a negative number, so that observed Frequency appears greater than what is generated

· When moving away, vo is negative and vs is positive

Sound Effects II

Changes in amplitude

Loudness (volume)

· As you already know, changes in sound volume are associated with changes in amplitude.

· In order to understand how a sound can change amplitude, we have to know a little more about waves.

Interference of Waves

· Two traveling waves can meet and pass through each other without being destroyed or even altered

· Waves obey the Superposition Principle

· If two or more traveling waves are moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point

· Actually only true for waves with small amplitudes

Constructive Interference

· Two waves, a and b, have the same frequency and amplitude· Are in phase

· The combined wave, c, has the same frequency and a greater amplitude

Constructive Interference in a String

· Two pulses are traveling in opposite directions· The net displacement when they overlap is the sum of

the displacements of the pulses· Note that the pulses are unchanged after the

interference

Destructive Interference

· Two waves, a and b, have the same amplitude and frequency

· They are 180° out of phase

· When they combine, the waveforms cancel

Destructive Interference in a String

· Two pulses are traveling in opposite directions· The net displacement when they overlap is decreased

since the displacements of the pulses subtract· Note that the pulses are unchanged after the

interference

I17.3, E17.1 andimation 2a

Interference of Sound Waves

· When constructive interference occurs, the amplitude increases, and the sound gets loud

· When destructive interference occurs, the amplitude decreases, and the sound diminishes

Constructive Interference

· Occurs when the source velocity exceeds the speed of the wave itself

· The circles represent the wave fronts emitted by the source

Constructive Interference

· At the edges, wave crests or compressions overlap, and so do wave troughs or rarefactions

· The most familiar example of this phenomenon is a bow wave from a ship

Shock Waves (Sonic Booms)

· In air, when a sound is made by something that travels faster than the speed of sound, the same thing happens

· Sound waves overlap in a cone shape.

Shock Waves, final

· Shock waves carry energy concentrated on the surface of the cone, with correspondingly great pressure variations

· A jet produces a shock wave seen as a fog

Constructive and Destructive Interference: Beats

· When two sound waves have frequencies that are close but not the same, sometimes the waves will constructively interfere, and sometimes they will destructively interfere.

· This results in a loud-soft-loud-soft pattern

Beats· Beats are alternations in loudness, due to interference· Waves have slightly different frequencies and the time

between constructive and destructive interference alternates· The beat frequency equals the difference in frequency

between the two sources:

Constructive and Destructive Interference: Standing Waves

· When a traveling wave reflects back on itself, it creates traveling waves in both directions

· The wave and its reflection interfere according to the superposition principle

· With exactly the right frequency, the wave will appear to stand still· This is called a standing wave

Standing Waves on a String

DO STANDING WAVE DEMO WITH SNAKEY SPRING NOW!!

Nodes

Anti-nodes

Natural Frequency

· Nearly every object will vibrate at a particular frequency that is unique to that object.

· This frequency is called the “natural frequency.”

· Tuning forks are made to have a specific natural frequency.

· Show Natural Frequency Demonstrator now!!

An Example of Resonance

· Pendulum A is set in motion

· The others begin to vibrate due to the vibrations in the flexible beam

· Pendulum C oscillates at the greatest amplitude since its length, and therefore frequency, matches that of A

Forced Vibrations

· A system with a driving force will force a vibration at its frequency

· When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance· Do forced vibration demo w/tuning forks

NOW!

Other Examples of Resonance

· Child being pushed on a swing

· Shattering glasses

· Walls of Jericho

· Upper deck of the Nimitz Freeway collapse due to the Loma Prieta earthquake

HARMONICS

For Honors Only

Standing Waves in Air Columns

· If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted

· If the end is open, the elements of the air have complete freedom of movement and an antinode exists

Tube Open at Both Ends

Resonance in Air Column Open at Both Ends

· In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency

Tube Closed at One End

Resonance in an Air Column Closed at One End

· The closed end must be a node

· The open end is an antinode

· There are no even multiples of the fundamental harmonic

Quality of Sound –Tuning Fork

· Tuning fork produces only the fundamental frequency

Quality of Sound – Flute

· The same note played on a flute sounds differently

· The second harmonic is very strong

· The fourth harmonic is close in strength to the first

Quality of Sound –Clarinet

· The fifth harmonic is very strong

· The first and fourth harmonics are very similar, with the third being close to them

Timbre

· In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound

· The quality depends on the mixture of harmonics in the sound

Pitch

· Pitch is related mainly, although not completely, to the frequency of the sound

· Pitch is not a physical property of the sound

· Frequency is the stimulus and pitch is the response· It is a psychological reaction that allows humans to place the

sound on a scale

The Ear

· The outer ear consists of the ear canal that terminates at the eardrum

· Just behind the eardrum is the middle ear

· The bones in the middle ear transmit sounds to the inner ear

Frequency Response Curves

· Bottom curve is the threshold of hearing· Threshold of hearing is

strongly dependent on frequency

· Easiest frequency to hear is about 3300 Hz

· When the sound is loud (top curve, threshold of pain) all frequencies can be heard equally well