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Physics of Sound

Physics of Sound. Logarithms. Do you know how to use your calculator? Find the following functions + , - , x , / , ^ , log The log is the exponent to which 10 is raised, representing a number. Antilogarithm. The antilog is 10 raised to the x power, or 10 x. Logarithms.

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Physics of Sound

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  1. Physics of Sound

  2. Logarithms • Do you know how to use your calculator? Find the following functions + , - , x , / , ^ , log The log is the exponent to which 10 is raised, representing a number

  3. Antilogarithm The antilog is 10 raised to the x power, or 10x

  4. Logarithms • Solve the following together: • Log (20) = ___________ • Log (400) = ____________ • Solve on your own: • Log (0.5) = ____________ • Log 2 = _____________

  5. Antilogarithms • Solve the following together: • X = 2 => _______________ • X = 4.3 => _______________ • Solve on your own: • X = 8.5 => _____________ • X = 9.0 => _____________

  6. What is sound? • Any change in air pressure • The molecules in the air exerts a pressure of over 1 ton per square foot on our ears • Must be a rapid change in sound pressure to be heard, a small rapid change will create noise • Travels as sound waves

  7. Frequency of Sound • Rate at which complete high and low pressure regions are produced by the sound source. • 1000 cycles per second is 1000 high and low pressure regions passing a point in one second. This is called 1000 Hertz (Hz) or 1 kHz.

  8. Speech frequencies • Speech frequencies: generally regarded to be 500 to 3000 hertz • Frequency range of perceivable sound: 20 Hz to 15,000 to 20,000 Hertz. • Tuning forks

  9. Tone and Noise • Tuning fork – pure tone and related frequencies • We cannot see the tines moving back and forth because they are moving back and for the too quickly. Two-hundred cycles a second is too fast to see. • Noise – random frequencies

  10. Noise travels through a medium • A vibrating object creates a disturbance that travels through a medium • A train’s noise can travel through the steel tracks by creating sound waves • The vibrations of a speaker creates sound waves • Frequency is the number of complete back and forth vibrations per second

  11. Noise travel • Vibrational motion of the medium is set up by the object. • The vibrations set the molecule of the medium into motion. • The motion of the molecule in the medium sets the molecule next to it, in motion. • The transfer of energy continues as the vibration of one molecule sets the next molecule into motion.

  12. Sound wave is a pressure wave • Thus an instrument can be used to measure the oscillations of high and low pressure variations in the pressure. • These oscillations are shown as the typical sine wave that you may have seen

  13. Wavelength • Distance which a disturbance travels along the medium in one complete wave cycle. • Measured from one wave trough or crest to the next wave trough or crest, in a transverse wave. It is from one wave compression to the next wave compression in a longitudinal wave • With a pressure wave it is from one high pressure region to the next high pressure region

  14. Speed of Sound • Sound waves are pressure disturbances traveling through a medium by means of particle interaction • How fast the disturbance is passed from particle to particle determines the speed of sound. • How easily the medium transfers the disturbance determines the speed, which is measured in feet per second (ft/sec)

  15. Speed of Sound • Speed is equal to distance traveled per unit time. • Speed = distance/time • If a sound waves travels 2,300 feet in 2 seconds the sound is traveling at 1,150 ft/sec • Examples of sound travel would be the time it takes for thunder to reach the observer and an echo

  16. Speed of Sound • The speed depends on the properties of the medium, the elastic properties are much greater than are the inertial properties. • Thus longitudinal sound waves will travel faster in solids than in liquids, and longitudinal sound waves will travel faster in liquids than in gases

  17. Speed of Sound in air • The speed of sound in air will depend on temperature and pressure of the air. The relationship is: C = 1054 f/s + (1.07 f/s/oF)xT

  18. Speed of Sound • At 72 oF, the speed of sound is 1,130 f/s • The delay between lightning and thunder. • Light travels 980,000,000 f/s or reaches the observer in almost no time. • The time delay of an echo is the same phenomenon, the distance of a reflecting surface can be determined by the time it takes for the echo to return

  19. Speed of Sound • The speed of sound in different mediums at standard conditions: • In air : the velocity is 1,130 f/s • In water: the velocity is 4,700 f/s • In wood: the velocity is 13,000 f/s • In steel: the velocity is 16,500 f/s

  20. Speed, frequency and wavelength • The mathematical relationship between the three is: C = λ x f The speed is a constant based on the properties of the medium. The length of a wave will vary with the frequency.

  21. Speed, frequency and wavelength At standard conditions, the speed of sound is 1,130 f/s. Say we have a 440 hertz frequency pure tone sound, what is the wavelength of the sound? C = λ x f λ = C / f λ = 1,130 / 440 λ = 2.57 feet

  22. Speed, frequency and wavelength • How about air at 1,000 oF as part of an exhaust stream? • Find the speed of sound traveling through the exhaust? C = 1,054 f/s + (1.07 f/s)x oF C = 1,054 + 1.07*1,000 C = 1,054 + 1070 = 2,124 f/s

  23. Speed, frequency and wavelength • Engine rotating at 3,000 rpm and has 4 cylinders 3,000 * 4 = 12,000 rounds per minute Which equals 200 rounds per second (Hz) What is the frequency of this sound? λ = C / f λ = 2,124 / 200 λ = 10.62 ft

  24. Speed, frequency and wavelength • What is the wavelength of the following frequencies? (at standard conditions) • λ20 hz = ________ remember: λ = C/f • λ1000 hz = ________ • λ16000 hz = ________

  25. Period • The period is the time for one complete cycle of pressure transition. It is the reciprocal of the frequency. T (sec) = 1/f The period of a 1000 Hz sound wave is: T = 1/f = 1/1000 = 0.001 seconds

  26. Period • What is the period of a 20 Hz and a 16,000 Hz wave? T20 Hz = 1/f = T16000 Hz = 1/f =

  27. Period • Below 20 Hz – infrasound • Above 20,000 Hz – ultrasound • Dogs – 50 Hz to 45,000 Hz • Cats – 45 Hz to 85,000 Hz • Bats – to 120,000 Hz • Dolphins – 200,000 Hz • Elephant – down to 5 Hz and up to 10,000 Hz

  28. Sound Waves • A pure tone (tuning fork) sound introduced into the room will create a change in the molecules in the room. • At 440 Hz the molecules will bunch up every 3 feet • Also there will be a net drift of molecules from the bunched up section to the section where the molecules are further apart. • The wave is moving toward me at 1,130 f/s

  29. Sound Waves • The sound wave is traveling toward me however, the molecules are not moving toward me. • An example would be a garden hose, when I shake it a snaky wave travels away, however, the hose is not moving only the wave energy is moving along it. • Other examples would include: sound, water, and football fans

  30. Sound Waves • Mechanical waves – they require a medium to transfer energy. So sound will not transfer through a vacuum. • Slinky demo • Pulse and a wave – moves one coil at a time • Medium is the slinky. In water it is the water, at a concert it is the air, at a football game it’s the fans in the stadium

  31. Intensity • The amount of energy which is transported past a given area of the medium per unit time • Intensity = energy / (time x area) • Since power is energy per unit time, it can also be written as: • Intensity = power / area • Typical units are Watts/meter2

  32. Intensity • Inverse square relationship • The mathematical relationship of intensity and the distance from the source • As you move away from the source (larger distance) the area gets larger and the intensity will decrease. • If the distance from a source doubles the intensity will decrease by a factor of 4.

  33. Threshold of Hearing • Humans can detect sound of very low intensity. The faintest sound which the ear can detect has an intensity of 1x10-12 W/m2. • At this level sound will displace particles of air by a mere one-billionth of a centimeter.

  34. Loudness • Loudness of a noise is a more subjective response. Factors that affect the perception of loudness includes age and frequency

  35. Sound Intensity • The average rate at which sound energy is flowing through a unit area • Intensity can be measured by means of a twin microphone probe, with signal processing by a microprocessor controlled cross correlation spectrum analyzer • Measurement of intensity is very useful in industrial noise situations

  36. Decibels • The decibel scale is a logarithmic scale. The logarithmic scale is based on multiples of 10. • A sound which is 10 times more intense is assigned a sound level of 10 dB. • A sound which is 100 times more intense is assigned a sound level of 20 dB. • A sound which is 1000 times more intense is assigned a sound level of 30 dB.

  37. Decibels • Threshold of hearing 0 dB • Whisper 20 dB • Normal conversation 60 dB • Street traffic 70 dB • Vacuum cleaner 80 dB • Walkman at max setting 100 dB • Threshold of Pain 130 dB • Military Jet Takeoff 140 dB

  38. Sound Pressure and Sound Pressure Level • Sound pressure is the root mean square (rms) value of the pressure changes above and below atmospheric when used to measure steady state noise. • The sound pressure level is the ratio expressed in decibels (dB) of the rms pressure to a reference rms pressure.

  39. Sound Pressure Level • Sound pressure level (Lp) is: Lp = 10 log (P / Po)2 = 20 log (P / Po) Where : Po= the reference sound pressure of 2 x 10-5 N/m2 Lp = sound pressure level in dB P = rms sound pressure in N/m2

  40. Sound Pressure Level For a sound source having a sound pressure of 1 N/m2, what is the sound pressure level in dB? Lp = 20 log (P/Po) = 20 log ((1 N/m2)/(2x10-5 N/m2) = 20 log (0.5 x 105) = 94 dB

  41. Sound Pressure Level If the sound source has a sound pressure of 2x10-3 N/m2, what is the sound pressure level in dB?

  42. Sound Pressure Level If the sound source has a sound pressure of 2x10-3 N/m2, what is the sound pressure level in dB? Lp = 20 log (P/Po) = 20 log ((2x10-3 N/m2)/(2x10-5 N/m2) = 20 log (1 x 102) = 40 dB

  43. Sound Pressure Level Weighted sound levels Fletcher-Munson curves. Ear is most sensitive around 2 to 5 kHz

  44. Decibel Addition To add individual sound levels the equation to add these is: LT = 10log(10L1/10+10L2/10+10L3/10+…+10Ln/10) Example: Two machines each operate at 93 dB at a given location. What is the sound pressure level if both machines are on?

  45. Decibel Addition Add to sound pressure levels of 93 dB together LT = 10log(10L1/10 + 10L2/10) LT = 10log(1093/10 + 1093/10) LT = 10log(2 x 109.3) = 96 dB

  46. Decibel Addition Exercise: Three machines have the following sound pressure levels at a given measurement location: 95, 96, 100 dB What is the resulting sound pressure level if all three machines are on?

  47. Decibel Addition Rule of thumb (can only be used when a limited number of sources are added together) 0 dB difference add 3 dB to the higher value 1-1.5 dB difference add 2.5 dB 2-3 dB difference add 2 dB 3.5 to 4.5 dB add 1.5 dB 5 to 7 dB add 1 dB 7.5 to 13 dB add 0.5 dB

  48. Decibel Addition • Using the rule of thumb in the previous exercise, find the total sound pressure level:

  49. Sound Pressure Level in decibels of common sources of noise See page 38 and 39 in your manual Examples: refrigerator 50 dB rainfall 50 dB doorbell 80 dB

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