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Fundamentals of Noise: Understanding Sound Propagation and Measurement

Discover the basics of noise, sound propagation through mediums, speed of sound, measurement techniques, sound pressure levels, decibel scale, sound intensity, frequency bands, and more. Gain insights into the science behind noise and its effects on our surroundings.

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Fundamentals of Noise: Understanding Sound Propagation and Measurement

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  1. FUNDAMENTALS OF NOISEDr. ASHISH K DARPE ASSISTANT PROFESSOR DEPARTMENT OF MECHANICAL ENGINEERING IIT DELHI

  2. Sound is a sensation of acoustic waves (disturbance/pressure fluctuations setup in a medium) Unpleasant, unwanted, disturbing sound is generally treated as Noise and is a highly subjective feeling

  3. Sound is a disturbance that propagates through a medium having properties of inertia ( mass ) and elasticity. The medium by which the audible waves are transmitted is air. • Basically sound propagation is simply the molecular transfer of motional energy. Hence it cannot pass through vacuum. Guess how much is particle displacement?? 8e-3nm to 0.1mm Frequency: Number of pressure cycles / time also called pitch of sound (in Hz)

  4. The disturbance gradually diminishes as it travels outwards since the initial amount of energy is gradually spreading over a wider area. If the disturbance is confined to one dimension ( tube / thin rod), it does not diminish as it travels ( except loses at the walls of the tube )

  5. Speed of Sound The rate at which the disturbance (sound wave) travels Property of the medium Alternatively, • c – Speed of sound P0, 0 - Pressure and Density • - Ratio of specific heats R – Universal Gas Constant T – Temperature in 0K M – Molecular weight Speed of Light: 299,792,458 m/s Speed of sound 344 m/s

  6. Sound Measurement • Provides definite quantities that describe and rate sound • Permit precise, scientific analysis of annoying sound (objective means for comparison) • Help estimate Damage to Hearing • Powerful diagnostic tool for noise reduction program: Airports, Factories, Homes, Recording studios, Highways, etc.

  7. Quantifying Sound Acoustic Variables: Pressure and Particle Velocity Root Mean Square Value (RMS) of Sound Pressure Mean energy associated with sound waves is its fundamental feature energy is proportional to square of amplitude

  8. RANGE OF PRESSURE Range of RMS pressure fluctuations that a human ear can detect extends from 0.00002 N/m2 (threshold of hearing) to 20 N/m2 (sensation of pain) 1000000 times larger Atmospheric Pressure is 105N/m2 so the peak pressure associated with loudest sound is 3500 times smaller than atm.pressure The large range of associated pressure is one of the reasons we need alternate scale

  9. dB SCALE Human ear responded logarithmically to power difference Alexander Graham Bell invented a unit Bel to measure the ability of people to hear Power Ratio of 2 = dB of 3 Power Ratio of 10 = dB of 10 Power Ratio of 100 = dB of 20 In acoustics, multiplication by a given factor is encountered most W1=W2*n So, Log10W1= Log10W2 + Log10n Thus, if the two powers differ by a factor of 10 (n=10), the difference between the Log values of two power quantities is 1Bel

  10. Decibel 10Log10W1= 10Log10W2 + 10Log10n to avoid fractions Now we have above quantities in deciBel, 10dB=1Bel deciBels are thus another way of expressing ratios Electrical Power Sound Power r - acoustic impedance 20Log10V1= 20Log10V2 + 20Log10n(1/2) 20Log10P1= 20Log10P2 + 20Log10n(1/2)

  11. Sound Pressure Level 20Log10P1= 20Log10P2 + 20Log10n(1/2) 20Log10(P1/P2) = 20Log10n(1/2) n: Ratio of sound powers 20Log10n(1/2) is still in deciBel, defined as Sound Pressure Level Sound pressure level is always relative to a reference In acoustics, the reference pressure P2=2e-5 N/m2 or 20Pa (RMS) SPL=20Log10(P1/2e-5) P1 is RMS pressure

  12. Sound Pressure Level Corresponding to audio range of Sound Pressure 2e-5 N/m2 - 0 dB 20 N/m2 - 120 dB Normal SPL encountered are between 35 dB to 90 dB For underwater acoustics different reference pressure is used Pref = 0.1 N/m2 It is customary to specify SPL as 52dB re 20Pa

  13. Sound Intensity

  14. Sound Intensity A plane progressive sound wave traveling in a medium (say along a tube) contains energy and rate of transfer of energy per unit cross-sectional area is defined as Sound Intensity Hold true also for spherical waves far away from source For air, 0c  415Ns/m3 so that

  15. COMBINATION OF SEVERAL SOURCES Total Intensity produced by several sources IT=I1+ I2+ I3+… Usually, intensity levels are known (L1, L2,…)

  16. COMBINATIONS OF SOURCES If intensity levels of each of the N sources is same, Thus for 2 identical sources, total Intensity Level is 10Log2 i.e., 3dB greater than the level of the single source For 2 sources of different intensities: L1 and L2 L1=60dB, L2=65.5dB LT=66.5dB L1=80dB, L2=82dB LT=84dB

  17. FREQUENCY & FREQUENCY BANDS Frequency of sound ---- as important as its level Sensitivity of ear Sound insulation of a wall Attenuation of silencer all vary with freq. <20Hz 20Hz to 20000Hz > 20000Hz Infrasonic Audio Range Ultrasonic

  18. Frequency Composition of Sound Pure tone Musical Instrument For multiple frequency composition sound, frequency spectrum is obtained through Fourier analysis

  19. A1 Amplitude (dB) f1 Frequency (Hz) Complex Noise Pattern produced by exhaust of Jet Engine, water at base of Niagara Falls, hiss of air/steam jets, etc No discrete tones, infinite frequencies Better to group them in frequency bands – total strength in each band gives measure of sound Octave Bands commonly used (Octave: Halving / doubling)

  20. OCTAVE BANDS 1= 1 1x2=2 2x2=4 4x2=8 8x2=16 16x2=32 32x2=64 64x2=128 128x2=256 256x2=512 512x2=1024 10 bands(Octaves) For convenience Internationally accepted ratio is 1:1000 (IEC Recommendation 225) Center frequency of one octave band is 1000Hz Other center frequencies are obtained by continuously dividing/multiplying by 103/10 starting at 1000Hz Next lower center frequency = 1000/ 103/10  500Hz Next higher center frequency = 1000*103/10  2000Hz International Electrotechnical Commission

  21. Octave Filters

  22. Instruments for analysing Noise Constant Bandwidth Devices Proportional Bandwidth Devices Absolute Bandwidth = fU - fL= fL n=1 for octave, n=3 for 1/3rd octave % Relative Bandwidth = (fU-fL/ fc) = 70.7% If we divide each octave into three geometrically equal subsections, i.e., These bands are thus called 1/3rd octave bands with % relative bandwidth of 23.1% For 1/10th Octave filters, % relative bandwidth of 5.1%

  23. Octave and 1/3rd Octave band filters mostly to analyse relatively smooth varying spectra If tones are present, 1/10th Octave or Narrow-band filter be used

  24. INTENSITY SPECTRAL DENSITY Acoustic Intensity for most sound is non-uniformly distributed over time and frequency Convenient to describe the distribution through spectral density I Intensity f1 f2 Frequency (Hz)  is the intensity within the frequency band Δf=1Hz For most noise, the instantaneous spectral density (t) is a time varying quantity, so that  in this expression is average value taken over a suitable period τ so that =< (t)>τ So, many acoustic filters & meters have both fast (1/8s) and slow (1s) integration times (For impulsive sounds some sound meters have I characteristics with 35ms time constant)

  25. Intensity Spectrum Level (ISL) DeciBel measure of is the Intensity Spectrum Level (ISL) If the intensity is constant over the frequency bandwidth w (= f2- f1), then total intensity is just I=  w and and Intensity Level for the band is If the ISL has variation within the frequency band (w), each band is subdivided into smaller bands so that in each band ISL changes by no more than 1-2dB

  26. IL is calculated and converted to Intensities Ii and then total intensity level ILtotal is as SPL and IL are numerically same, Can be written as Thus, when intensity level in each band is known, total intensity level can be estimated PSL (Pressure Spectrum Level) is defined over a 1Hz interval – so the SPL of a tone is same as its PSL

  27. Combining Band Levels and Tones SPL = PSL + 10 log w For pure tones, PSL = SPL so, two SPL of the tones is 63 & 60 dB For the broadband noise, SPL = PSL + 10 log w = PSL + 10 log 100 SPL = 60 dB Thus the overall band level = Band level of broadband noise + Level of tones = 60 + 63 + 60 = 64.7 + 60 ≈ 66 dB

  28. Sound Power Intensity : Average Rate of energy transfer per unit area Sound Power Level: dB Reference Power Wref =10-12 Watt Peak Power output: Female Voice – 0.002W, Male Voice – 0.004W, A Soft whisper – 10-9W, An average shout – 0.001W Large Orchestra – 10-70W, Large Jet at Takeoff – 100,000W 15,000,000 speakers speaking simultaneously generate 1HP

  29. Recap • Sound Measurement –Amplitude/Frequency • Sound Pressure, Intensity, Power, ISL, PSL

  30. Radiation from Source Point Source (Monopole) Radiates sound waves equally in all directions (spherical radiation) W: is acoustic power output of the source; power must be distributed equally over spherical surface area Inverse Square Law Constant term Depends on distance from source When distance doubles (r=2r0) ; 20log 2 + 20log r0 means 6dB difference in the Sound Intensity Level

  31. If the point source is placed on ground, it radiates over a hemisphere, the intensity is then doubled and

  32. Line Source (Long trains, steady stream of traffic, long straight run of pipeline) If the source is located on ground, and has acoustic power output of Wper unit length radiating over half the cylinder Intensity at radius r, When distance doubles; 10log 2 + 10log r means 3dB difference in the Sound Intensity Level

  33. VALIDITY OF POINT SOURCE In free field condition, Any source with its characteristic dimension small compared to the wavelength of the sound generated is considered a point source Alternatively a source is considered point source if the receiver is at large distance away from the source Some small sources do not radiate sound equally in all directions Directivity of the source must be taken into account to calculate level from the source power

  34. DIRECTIVITY OF SOUND SOURCE Sound sources whose dimensions are small compared to the wavelength of the sound they are radiating are generally omni-directional; otherwise when dimensions are large in comparison, they are directional

  35. Directivity Factor & Directivity Index Directivity Factor Directivity Index Rigid boundaries force an omni-directional source to radiate sound in preferential direction

  36. EFFECT OF HARD REFLECTING GROUND Radiated Sound Power of the source can be affected by a rigid, reflecting planes Strength and vibrational velocity of the source does not change but the hard reflecting plane produces double the pressure and four-fold increase in sound intensity compared to monopole (point spherical source) If source is sufficiently above the ground this effect is reduced

  37. I=0 Uniform sound energy density Free Field Condition Diffuse Field

  38. MWL Lab, KTH Sweden Finding sound power (ISO 3745)

  39. Measurements made in semi-reverberant and free field conditions are in error of 2dB

  40. Noise Mapping Noise Contours

  41. Environmental Effects Wind Gradient Hot Sunny Day Velocity Gradient (-) Temperature Gradient Cool Night Wind & Temp effects tend to cancel out Increase or decrease of 5-6dB

  42. Environmental Effects…

  43. HUMAN PERCEPTION

  44. The Human Ear Outer Ear: Pinna and auditory canal concentrate pressure on to drum Middle Ear: Eardrum, Small Bones connecting eardrum to inner ear Inner Ear: Filled with liquid, cochlea with basilar membrane respond to stimulus of eardrum with the help of thousands of tiny, highly sensitive hair cells, different portions responding different frequencies of sound. The movement of hair cells is conveyed as sensation of sound to the brain through nerve impulses Masking takes place at the membrane; Higher frequencies are masked by lower ones, degree depends on freq.difference and relative magnitudes of the two sounds

  45. SOUND BITS Unless there is a 3 dB difference in SPL, human beings can not distinguish the difference in the sound Sound is perceived as doubled in its loudness when there is 10dB difference in the SPL. (Remember 6dB change represents doubling of sound pressure!!) Ear is not equally sensitive at all frequencies: highly sensitive at frequencies between 2kHz to 5kHz less at other freq. This sensitivity dependence on frequency is also dependent on SPL!!!!

  46. RESPONSE OF HUMAN EAR Loudness Level (Phon) Equal to numerical value of SPL at 1000Hz 0Phon: threshold of hearing Loudness Level (Phon) useful for comparing two different frequencies for equal loudness But, 60Phon is still not twice as loud as 30Phon Doubling of loudness corresponds to increase of 10Phon Equal Loudness Contours for pure tones, Free Field conditions

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