Sound Waves Vibration of a tuning fork http://www.ndt-ed.org/EducationResources/HighSchool/Sound/hs_sound_index.htm

Pressure Waves Sound waves is usually analyzed from the point of view of pressure because the pressure is easier to measure than displacement. Compression (pressure higher) Rarefaction (pressure lower) Atmospheric pressure

Pressure and Displacement in Sound Waves A sound wave can be described in terms of displacements of particles in the medium or in terms of pressure fluctuations. Displacement Pressure fluctuation Position The displacement graph is π/2 out of phase with the pressure graph. http://squ1.com/archive/index.php?sound/properties.html

Variation of the air pressure in an air column

Pressure and displacement in an air column When the air is constrained to a node, the air motion will be alternately squeezing toward that point and expanding away from it, causing the pressure variation to be at a maximum. http://www.walter-fendt.de/ph11e/stlwaves.htm

Frequency Spectrum of Sound Waves Frequency in Hz on a log scale 1 10 102 103 104 105 106 107 108 /Hz 20 kHz 20 Hz Used in medical diagnosis Subsonic Range of sound frequencies heard by human ears Ultrasound Note that the audible range varies somewhat from one individual to another.

The Speed of Sound Typically there are two essential types of properties which effect wave speed. Inertial properties (e.g. mass density, ) The greater the inertia the slower the wave. Elastic properties (e.g. Young modulus, E) The higher the elasticity the faster the wave. Speed of Sound in a long solid rod Where E is the Young modulus and  is the density of the solid rod.

Speed of Sound in air The speed of a sound wave in air depends upon the properties of the air the temperature and the temperature will affect the strength of the particle interactions (an elastic property). the pressure The pressure of air (like any gas) will affect the mass density of the air (an inertial property). v = 331 + 0.61 TC (m s-1)

Measuring the Speed of Sound in Air (1) http://hyperphysics.phy-astr.gsu.edu/hbase/waves/kundtosc.html The speed of sound in air can be measured by Stationary waves pattern established between a loudspeaker and a metal reflector. Using a resonance tube (or Kundt’s tube) Glass Tube Signal generator

Measuring the Speed of Sound in Air (2) http://www.picotech.com/applications/sound.html

Measuring the speed of sound using echoes http://serc.carleton.edu/quantskills/teaching_methods/uncertainty/examples/example2.html http://www.cdli.ca/courses/phys2204/unit04_org02_ilo02/b_activity.html

Speed of Sound in Various Materials Speed of sound /m s-1 Air (0 oC) 331 Air (20 oC) 344 Helium (20 oC) 999 Hydrogen (20 oC) 1330 Water (0 oC) 1400 Water (20 oC) 1480 Mercury (20 oC) 1450 Aluminium 6420 Steel 5940 Lead 1960

Effect of temperature and relative humidity on the speed of sound in air

Loudness Loudness is a sensation in the consciousness of a human being. The assessment of loudness is controlled by (1) The sound wave intensity, which depends on (a) the square of the amplitude, (b) the frequency, (c) the speed, (d) the density of the medium. (2) The sensitivity of the hearer to the particular frequency being sounded.

Energy Transport and the Amplitude of a Wave The energy transported by a wave is directly proportional to the square of the amplitude of the wave. E  A2

Sound Intensity The sound intensity in a specified direction is the rate of sound energy flowing through a unit area normal to that direction. The sound intensity is normally measured in watt per square metre (W/m2). A Energy flow Unit : W m-2

Variation of Intensity with Distance (1) The intensity decreases away from the source because - the energy is distributed through a larger volume, (For a point source and isotropic medium the intensity will obey the inverse square law.) - of attenuation: the wave energy is gradually converted by an imperfectly elastic medium into the internal energy of the medium’s molecules.

Variation of Intensity with Distance (2) As the wave moves outward, the energy it carries is spread over a larger and larger area since the surface area of a sphere of radius r is 4r2. r If the power output is P, then the average intensity, through a sphere with radius r is

Variation of Intensity with Distance (3) Intensity level Distance If a source of sound can be considered as a point, where r is the distance from the source.

Intensity Level (Decibel) The intensity level  of a sound wave is defined by where I = the intensity of sound, Io= 1 pW m-2 (Threshold of hearing) Unit : decibel (dB) The dB-scale is a logarithmic, the reason for measuring sound this way is that our ears (and minds) perceive sound in terms of the logarithm of the sound pressure, rather than the sound pressure itself. http://www.teachersdomain.org/resource/lsps07.sci.phys.energy.amplitude/

Difference in Sound Intensity Level Consider two loudspeakers playing sounds with power P1 and P2 respectively. The difference in decibels between the two is defined to be http://www.phys.unsw.edu.au/jw/dB.html#definitioin

Intensity of Various Sounds Source of the Sound Intensity Level/dB Intensity/W m-2 Jet plane at 30 m 140 100 Threshold of pain 120 1 Loud indoor rock concert 120 1 Siren at 30 m 100 1 × 10-2 Automobile moving at 90 km h-1 75 3 × 10-5 Busy street traffic 70 1 × 10-5 Ordinary conversation, at 50 cm 65 3 × 10-6 Quiet radio 40 1 × 10-8 Whisper 20 1 × 10-10 Rustle of leaves 10 1 × 10-11 Threshold of hearing 1 × 10-12

Sensitivity of Human Ear as a Function of Frequency http://www.phys.unsw.edu.au/jw/hearing.html Each curve represents sounds that seemed to be equally loud. Note that the ear is most sensitive to sounds of frequency between 2 kHz and 4 kHz.

Sound Proofing (1) Soundproofing of a room involves the isolation of that room from audible sound from the outside and may be taken to include the acoustic damping of the room itself. Preventing the entrance of sound from the outside is accomplished by -sealing openings, -making the walls absorbent of sound, and -minimizing the passage of sound energy through the solid structures of the walls.

Sound Proofing (2) Sound absorbing materials such as foam insulation in the walls help with both the sealing and absorbing of mid-range to high frequency sounds.