Wave Motions and SoundWave Motions and Sound

Investigation 4

Forces and elastic materials

Elastic material• Capable of recovering shape after deformation• Rubber ball versus lump of clay

Spring forces1. Applied force proportional to distance spring is

compressed or stretched2. Internal restoring force arises, returning spring

to original shape3. Restoring force also proportional to stretched or

compressed distance

Forces and vibrations

• Vibration - repetitive back and forth motion

• At the equilibrium position, spring is not compressed

• When disturbed from equilibrium position, restoring force acts toward equilibrium

• Carried by inertia past equilibrium to other extreme

• Example of “simple harmonic motion”

Describing vibrations

• Amplitude - maximum extent of displacement from equilibrium

• Cycle - one complete vibration

• Period - time for one cycle

• Frequency - number of cycles per second (units = hertz, Hz)

• Period and frequency inversely related

Waves

• Periodic (traveling) disturbances transporting energy

• Causes– Period motion disturbing surroundings– Pulse disturbance of short duration

• Mechanical waves– Require medium for propagation– Waves move through medium– Medium remains in place

Kinds of waves

Longitudinal waves• Vibration direction parallel to

wave propagation direction• Particles in medium move

closer together/farther apart• Example: sound waves • Gases and liquids - support

only longitudinal waves

Kinds of waves, cont.Transverse waves• Vibration direction perpendicular

to wave propagation direction• Example: plucked stringSolids - support both longitudinal

and transverse wavesSurface water waves• Combination of both• Particle motion = circular

Waves in air

• Longitudinal waves only

• Large scale - swinging door creates macroscopic currents

• Small scale - tuning fork creates sound waves

• Series of condensations (overpressures) and rarefactions (underpressures)

Hearing waves in air

Range of human hearing: 20-20,000 Hz

• Infrasonic– Below 20 Hz– Felt more than heard

• Ultrasonic– Dogs, cats, rats & bats– Used in imaging

• Mechanism in ear – Eardrum, bones, fluid

cell, hairs to nerve impulses…

Describing waves

Graphical representation

• Pure harmonic waves = sines or cosines

Wave terminology• Wavelength• Amplitude• Frequency • Period

Wave propagation speed

Sound waves

• Require medium for transmission

• Speed varies with– Inertia of molecules– Interaction strength– Temperature

• Various speeds of sound

Velocity of sound in air

• Varies with temperature• Warmer the air, greater the kinetic

energy of the gas molecules– Molecules of warmer air transmit sound

impulses from molecule to molecule more rapidly

– Greater kinetic energy sound impulse transmitted faster

• Increase factor (units!): 0.6 m/s/°C; 2.0 ft/s/°C

Visualization of waves

• Sound = spherical wave moving out from source

• Each crest = wave front

• Wave motion traced with wave fronts

• Far from source, wave front becomes planar

Refraction and reflection

• Boundary effects– Reflection - wave bounces off boundary– Refraction - direction of wave front changes– Absorption - wave energy dissipated

• Types of boundaries– Between different materials– Between regions of the same material under

different conditions (temperature, pressure)

Refraction

• Bending of wave fronts upon encountering a boundary– Between two different

media– Between different

physical circumstances in the same medium

• Example - temperature gradient in air

Reflection

• Wave rebounding off boundary surface

• Reverberation - sound enhancement from mixing of original and reflected sound waves

• Echo – Can be distinguished by

human ear if time delay between original and reflected sound is greater then 0.1 s

– Used in sonar and ultrasonic imaging

Interference

• Two or more waves combine

• Constructive interference

• Peaks aligned with peaks; troughs aligned with troughs

• Total wave enhanced

Interference, cont.

• Destructive interference– Peaks aligned with

troughs– Cancellation leads to

diminished wave

• Beats– Overall modulation of

sound from mixing of two frequencies

– Beat frequency = difference in two frequencies

Energy and sound

• Intensity– Energy flowing (power) through a given area– Proportional to amplitude of sound wave,

squared – Units = W/m2

Loudness

• Subjective perception related to– Energy of vibrating object– Atmospheric conditions– Distance from source

• Intensity range of human hearing (decreases with age!)

Decibel scale

• Better reflects nonlinear relationship between perceived loudness and intensity

• Logarithmic scale means simpler numbers

Resonance

• Excitation of natural frequency (“resonant frequency”) by a matching external driving frequency

• Examples– Pushing a swing– Tuned boxes and

tuning forks– Earthquake resistant

architecture

Sources of sound

• Vibrating objects• Source of all sound• Irregular, chaotic vibration produces

noise• Regular, controlled vibration can

produce music• All sound is a combination of pure

frequencies

Vibrating strings

• Important concepts - strings with fixed ends–More than one wave can be present at

the same time–Waves reflected and inverted at end

points – Interference occurs between incoming

and reflected waves

Vibrating strings, cont.

• Standing waves• Produced by

interferences at resonant frequencies

• Nodes - destructive interference points

• Anti-nodes - points of constructive interference

Resonant frequencies of strings

• Fundamental - lowest frequency

• Higher modes - overtones (first, second, …)

• Mixture of fundamental and overtones produces “sound quality” of instrument

• Formula for resonant frequencies

Sounds from moving sources

• Doppler effect• Wave pattern

changed by motion of source or observer

• Approaching - shifted to higher frequency

• Receding - shifted to lower frequency

• Supersonic speed - shock wave and sonic boom produced

Problem1

• A vibrating system has a period of 0.5s. What is the frequency in Hz?

For this problem all the ones to follow, answer on your own sheet of paper and show your work. Put your own name at the top although you may work as a team. Due today. 2 pts. Each.

Problem 2

• A sound wave with a frequency of 260 Hz has a wavelength of 1.27m. With what speed would you expect this sound wave to move?

Problem 3

• In general, the human ear is most sensitive to sounds at 2500 Hz. Assuming that sound moves at 330m/s, what is the wavelength of sounds to which people are most sensitive?

Problem 4

• The human ear can distinguish a reflected sound pulse from the original sound pulse if 0.10s or more time elapses between two sounds. What is the minimum distance to a reflecting surface from which we can hear an echo if the speed of sound is 343 m/s?

Problem 5

• A tuning fork vibrates 440.0 times a second, producing sound waves with a wavelength of 78.0cm. What is the velocity of these waves?

Problem 6

• The air temperature is 80deg F during a thunderstorm, and the thunder was timed 4.63s after lightning was seen. How many feet away was the lightning strike?

Problem 7

• Why did the Apollo astronauts talk to each other while on the moon with radios? (Or, what we today would call cell phones)

• How did they communicate with each other in the Lunar Module?

Problem 8

• What is resonance?

Problem 9

• What is the Doppler Effect?

• Provide an example using sound waves.

Problem 10• During the days of the European Concorde airliner, people could experience sonic booms near the New York, London, and Paris airports: therefore, a not uncommon experience. Concorde no longer flies. What would you have to do, where would you go to experience one today?