Intro to Sound Sound Waves Sound waves are

Intro to Sound

Sound Waves Sound waves are produced by a vibrating object. Sound waves are longitudinal mechanical waves. Often demonstrated with a tuning fork – as tines vibrate, they disturb the surrounding air molecules

Sound as a Longitudinal Wave Individual particles of medium move parallel to the direction of the wave As particles push on adjacent particles, some regions are created where particles are pressed together (high pressure) and in some regions they are spread apart (low pressure).

Sound waves Compressions – the areas of high pressure Rarefactions – the areas of low pressure Since there is a repeating pattern of compressions and rarefactions, sound waves are also called “pressure waves” A wavelength is the distance from compression to compression (or rarefaction to rarefaction)

Transverse vs. Longitudinal Waves traveling through a solid medium can be either transverse or longitudinal Waves traveling through a liquid or gas are ALWAYS longitudinal

Transmission of pulse in different mediums Wave speed differs in different types of media Waves are faster in less dense media At the boundary, waves will either reflect back or transmit through the other medium

Sound Behaviors: Reflection of sound results in an echo Sound waves leave a source, travel a distance, and bounce back to the origin Animals, like bats, use echoes to locate prey Other uses include determining distances between objects, echocardiograms The distance the sound travels to get back to the origin is 2 x the distance between the sound source and boundary

Reflection Law of Reflection: The angle of incidence is equal to the angle of reflection

Sound Behavior: Refraction occurs when sound moves from one medium to another The wave bends, and the speed changes • Even when sound moves from warmer areas to cooler areas, refraction occurs

Sound Behavior: Diffraction occurs when sound waves pass through an opening or through a barrier Low pitched sound waves travel farther than high pitched sound waves Animals use diffraction for communication http: //video. nationalgeographic. com/video/animals/ mammalsanimals/elephant_african_vocalization/

Interference of sound waves causes beats Beats occur due to constructive and destructive interference between sound waves of very similar frequencies The beat frequency will be the difference in the 2 sound frequencies: Ex: 2 sound waves with frequencies of 256 Hz and 254 Hz will have a beat frequency of 2 Hz Humans can hear beats with frequencies of 7 Hz and below

Pitch and Frequency – how often the particles of the medium vibrate when a wave passes through the medium (Hz) Frequency and Period are inversely related: High frequency = short wavelength period Low frequency = long wavelength period The sensation of a frequency is referred to as the pitch High pitch = high frequency Low pitch = low frequency

Pitch and Frequency Certain sound waves when played/heard simultaneously will produce a pleasing sound are called “consonant” Such sound waves form the basis of intervals in music Any 2 sounds whose frequencies make a 2: 1 ratio are separated by an octave (one sound has twice the frequency of the other) Ex: sounds with frequencies of 512 Hz and 256 Hz

Intensity The human ear is sensitive to differences in pressure waves The AMPLITUDE of a sound wave determines its loudness or softness This means the more energy in a sound wave, the louder the sound Sound intensity is a measure of how much energy passes a given point in a time period Intensity is measured in decibels (db)

Intensity As sound waves travel through a medium, the intensity decreases with increasing distance from the source Intensity varies inversely with the square of the distance Ex: if distance doubles, the intensity goes down by 4 x

The Decibel Scale Based on powers of 10 Humans can hear a range of frequencies from 20 Hz to 20, 000 Hz The older you get, the hearing range shrinks Sound waves with frequencies below 20 Hz are called infrasonic Sound waves with frequencies above 20, 000 Hz are called ultrasonic

Hearing Range Frequencies http: //www. movingsoundtech. com/ http: //www. noiseaddicts. com/2009/03/can-you-hearthis-hearing-test/

Source of Sound Level (d. B) Increase over Threshold 0 d. B 0 Normal Breathing 10 d. B 10 Whisper 20 d. B 100 Normal Conversation 60 d. B 106 Busy street traffic 70 d. B 107 Vacuum cleaner 80 d. B 108 Average factory 90 d. B 109 IPod at maximum level 100 d. B 1010 Threshold of pain 120 d. B 1020 Jet engine at 30 m 140 d. B 1014 Perforation of eardrum 160 d. B 1016

Velocity (speed) of sound depends on the medium it travels through and the phase of the medium Sound travels faster in liquids than in air (4 times faster in water than air) Sound travels faster in solids than in liquids (11 times faster in iron than in air) Sound does not travel through a vacuum (there are no particles, so sound has no medium) Vsolid > vliquid>vgas

Velocity and Temperature In air at room temperature, sound travels at 343 m/s (at 20°C). This is about 766 mph. As temperature increases, the velocity of sound increases v=331 + (0. 6)T v= velocity of sound in air T=temperature of air in °C

Wave Equation

Example Problems: 1. Sound waves travel at approximately 340 m/s. What is the wavelength of a sound wave with a frequency of 20 Hz? 2. What is the speed of sound traveling in air at 28º C? 3. If the above sound wave has a frequency of 261. 6 Hz, what is the wavelength of the wave?

What is the Doppler Effect? http: //molebash. com/doppler/home. htm

Doppler Effect The Doppler effect is a change in the apparent frequency due to the motion of the source or the receiver Example: As an ambulance with sirens approaches, the pitch seems high. As the ambulance moves away the pitch lowers.

Doppler Effect Sound waves move out in all directions As the wave travels outward, the front of the wave bunches up, producing a shorter wavelength We hear a higher frequency

The back of the wave spreads out, producing a longer wavelength We hear a lower frequency http: //www. sounddogs. com/searchre sults. asp? Keyword=Doppler

Doppler Effect Example http: //www. animations. physics. unsw. edu. au/jw/dop pler. htm#example

• Observer A hears a low pitch (lower frequency) • Observer B hears the correct pitch (no change in frequency) • Observer C hears a high pitch (high frequency)

When the source goes faster, the wave fronts in the front of the source start to bunch up closer and closer together, until. . .

The object actually starts to go faster than the speed of sound. A sonic boom is then created.

Uses of the Doppler Effect Police use Doppler to measure your speed with radar A frequency is sent out with a radar gun The sound wave hits your car and bounces back to the police car Speed can be determined based on the frequency changes received Radar can be used to determine the speed of baseballs Astronomers can determine the distance to other galaxies Bats use Doppler to locate prey

Acoustics- field of study related to sound Acoustic designers try to maximize the quality of sound reaching the audience Control the size, shape, and material used They try and control the reflection

Sound and Hearing Acoustics is the branch of physics pertaining to sound The ear converts sound energy to mechanical energy to a nerve impulse that is then transmitted to the brain Our ears allow us to perceive changes in pitch Our ears are sensitive to a particular range of frequencies between 1, 000 – 4, 000 Hz.

The Outer Ear The outer ear consists of the earlobe and the ear canal Sound enters the outer ear as a pressure wave The outer ear provides protection to the middle ear and protects the eardrum

Sound starts at the Pinna

Then goes through the auditory canal

The Middle Ear The middle ear is an air-filled cavity that consists of an eardrum and three tiny, interconnected bones - the hammer, anvil, and stirrup. The eardrum is a very durable and tightly stretched membrane that vibrates as the incoming pressure waves reach The stirrup is connected to the inner ear

The sound waves will then vibrate the Tympanic Membrane (eardrum) which is made of a thin layer of skin.

The tympanic membrane will then vibrate three tiny bones: the Malleus (hammer), (hammer) the Incus (anvil), (anvil) and the Stapes (stirrup)

The Inner Ear The inner ear consists of a cochlea, the semicircular canals, and the auditory nerve The cochlea and the semicircular canals are filled with a water-like fluid The fluid and nerve cells of the semicircular canals provide no role in the task of hearing; they speed up the detection of sound

The stapes will then vibrate the Cochlea

Inside look of the Cochlea The stapes vibrates the cochlea The frequency of the vibrations will stimulate particular hairs inside the cochlea The intensity at which these little hairs are vibrated will determine how loud the sound is. The auditory nerve will then send this signal to the brain.

Standing Waves Standing waves are produced only at specific frequencies, called “harmonics” Different frequencies create different standing wave patterns:

1 st harmonic pattern 2 nodes and 1 antinode Simplest harmonic pattern Low frequencies 2 nd harmonic pattern 3 nodes and 2 antinodes 2 times the frequency as 1 st 3 rd harmonic pattern 4 nodes and 3 antinodes

Resonance

Natural Frequency Nearly all objects when hit or disturbed will vibrate. Each object vibrates at a particular frequency or set of frequencies. This frequency is called the natural frequency. If the amplitude is large enough and if the natural frequency is within the range of 20 -20000 Hz, then the object will produce an audible sound.

Factors Affecting Natural Frequency Properties of the medium Modification in the wavelength that is produced (length of string, column of air in instrument, etc. ) Temperature of the air

Timbre is the quality of the sound that is produced. If a single frequency is produced, the tone is pure (example: a flute) If a set of frequencies is produced, but related mathematically by whole-number ratios, it produces a richer tone (example: a tuba) If multiple frequencies are produced that are not related mathematically, the sound produced is described as noise (example: a pencil)

Resonance occurs when one object vibrates at the same natural frequency of a second object, forcing that second object to vibrate at the same frequency.

Types of Resonance is the cause of sound production in musical instruments. Energy is transferred thereby increasing the amplitude (volume) of the sound. Resonance takes place in both closed pipe resonators and open pipe resonators. Resonance is achieved when there is a standing wave produced in the tube.

Closed pipe resonator • open end of tube is anti-node • closed end of tube is node

Harmonics of Closed Pipe Resonance The shortest column of air that can have a pressure anti-node at the closed end a pressure node at the open end is ¼ wavelength long. This is called the fundamental frequency or first harmonic. As the frequency is increased, additional resonance lengths are found at ½ wavelength intervals. The frequency that corresponds to ¾ wavelength is called the 3 rd harmonic, 5/4 wavelength is called the 5 th harmonic, etc.

Open pipe resonator • both ends are open • both ends are anti-node

Harmonics of Open Pipe Resonance The shortest column of air that can have nodes (or antinodes) at both ends is ½ wavelength long. This is called the fundamental frequency or first harmonic. As the frequency is increased, additional resonance lengths are found at ½ wavelength intervals. The frequency that corresponds to a full wavelength is the second harmonic, 3/2 wavelength is the third harmonic, etc.

Problem 1. Tommy and the Test Tubes have a concert this weekend. The lead instrumentalist uses a test tube (closed end air column) with a 17. 2 cm air column. The speed of sound in the test tube is 340 m/s. Find the frequency of the first harmonic played by this instrument.

Solution L = λ/4 4 x L = λ 4 x. 172 =. 688 m v = f λ 340 = f (. 688) f = 494 Hz

Problems 2. Matt is playing a toy flute, causing resonating waves in a open-end air column. The speed of sound through the air column is 336 m/s. The length of the air column is 30. 0 cm. Calculate the frequency of the first, second, and third harmonics.

Solution L = λ/2 2 x L = λ 2 x. 30 =. 60 m v = f λ 336 = f (. 60) f = 560 Hz. (first harmonic) 2 nd harmonic = 560 + 560 = 1120 Hz. 3 rd harmonic = 1120 + 560 = 1680 Hz

Resonance in Music Forced Vibration- The vibration of an object that is made to vibrate by another vibrating object. Sympathetic vibrations- secondary vibrations caused by forced vibration of a first object. Sounding board- part of an instrument forced into vibration to amplify sound

Resonance can be dangerous Wind caused the Tacoma Narrows suspension bridge to vibrate at its natural frequency. The amplitude of the vibrations caused too much strain on the bridge until it collapsed.

Standing Waves are formed in the instrument due to vibrations When the natural frequency is hit the sound amplifies

Open Ended Wind Column Instrument Must be nodes at both ends

Closed Ended Wind Column Instrument There is an antinode at the closed end. Count standing waves by including the return trip.