# FUNDAMENTALS OF NOISE Dr. ASHISH K DARPE ASSISTANT PROFESSOR DEPARTMENT OF MECHANICAL ENGINEERING IIT DELHI.

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FUNDAMENTALS OF NOISE Dr. ASHISH K DARPE ASSISTANT PROFESSOR DEPARTMENT OF MECHANICAL ENGINEERING IIT DELHI

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

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. Frequency: Number of pressure cycles / time also called pitch of sound (in Hz) Guess how much is particle displacement?? 8e-3nm to 0.1mm

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 )

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

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.

Quantifying Sound 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 Acoustic Variables: Pressure and Particle Velocity

Range of RMS pressure fluctuations that a human ear can detect extends from 0.00002 N/m 2 (threshold of hearing) to 20 N/m 2 (sensation of pain) 1000000 times larger Atmospheric Pressure is 10 5 N/m 2 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 RANGE OF PRESSURE

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 W 1 =W 2 *n So, Log 10 W 1 = Log 10 W 2 + Log 10 n 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 dB SCALE

10Log 10 W 1 = 10Log 10 W 2 + 10Log 10 nto avoid fractions Now we have above quantities in deciBel, 10dB=1Bel deciBels are thus another way of expressing ratios Electrical Power Sound Power 20Log 10 V 1 = 20Log 10 V 2 + 20Log 10 n (1/2) 20Log 10 P 1 = 20Log 10 P 2 + 20Log 10 n (1/2) r - acoustic impedance Decibel

Sound Pressure Level 20Log 10 P 1 = 20Log 10 P 2 + 20Log 10 n (1/2) 20Log 10 (P 1 /P 2 ) = 20Log 10 n (1/2) 20Log 10 n (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 P 2 =2e-5 N/m 2 or 20  Pa (RMS) SPL=20Log 10 (P 1 /2e-5)P 1 is RMS pressure n: Ratio of sound powers

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

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 For air,  0 c  415Ns/m 3 so that Hold true also for spherical waves far away from source

COMBINATION OF SEVERAL SOURCES Total Intensity produced by several sources I T =I 1 + I 2 + I 3 +… Usually, intensity levels are known (L 1, L 2,…)

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: L 1 and L 2 COMBINATIONS OF SOURCES L 1 =60dB, L 2 =65.5dB L T =66.5dB L 1 =80dB, L 2 =82dB L T =84dB

FREQUENCY & FREQUENCY BANDS Frequency of sound ---- as important as its level Sensitivity of ear Sound insulation of a wall Attenuation of silencerall vary with freq. 20000Hz InfrasonicAudio RangeUltrasonic

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

Amplitude (dB) A1A1 f1f1 Frequency (Hz) Complex Noise Pattern 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) produced by exhaust of Jet Engine, water at base of Niagara Falls, hiss of air/steam jets, etc

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 10 3/10 starting at 1000Hz Next lower center frequency = 1000/ 10 3/10  500Hz Next higher center frequency = 1000*10 3/10  2000Hz International Electrotechnical Commission

Octave Filters

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

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

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  = 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) Intensity I f1f1 Frequency (Hz) f2f2 INTENSITY SPECTRAL DENSITY Acoustic Intensity for most sound is non-uniformly distributed over time and frequency Convenient to describe the distribution through spectral density  is the intensity within the frequency band Δf=1Hz

DeciBel measure of  is the Intensity Spectrum Level (ISL) If the intensity is constant over the frequency bandwidth w (= f 2 - f 1 ), then total intensity is justI=  wand and Intensity Level for the band is Intensity Spectrum Level (ISL) 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

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

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

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

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

Radiation from Source 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 Constant termDepends on distance from source When distance doubles (r=2r 0 ) ; 20log 2 + 20log r 0 means 6dB difference in the Sound Intensity Level Inverse Square Law Point Source (Monopole)

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

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 W per 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

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 VALIDITY OF POINT 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 DIRECTIVITY OF SOUND SOURCE

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

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 EFFECT OF HARD REFLECTING GROUND

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

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

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

Noise Mapping Noise Contours

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

Environmental Effects…

HUMAN PERCEPTION

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

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!!!! SOUND BITS

Equal Loudness Contours for pure tones, Free Field conditions 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

Weighting Characteristics A-weighting: 40Phon equal loudness level contour C-weighting: 90Phon equal loudness level contour D-weighting for Aircraft Noise

BASIC SOUND LEVEL METER

LOUDNESS INDEX Direct relationship between Loudness Level ‘P’ (Phons) and Loudness Index ‘S’ (Sones) 8 Sones is twice as loud as 4 Sones

Hearing Damage Potential to sound energy depends on its level & duration of exposure Equivalent Continuous Sound Level (L eq ) t j : Fraction of total time duration for which SPL of L j was measured Total time interval considered is divided in N parts with each part has constant SPL of L j

Integrating Sound Level Meter for randomly varying sound e.g., 60sec L eq Sound Exposure Level (SEL) Constant level acting for 1sec that has the same acoustic energy as the original sound Vehicle passing by; Aircraft flying over…

Noise Dose Meters display Noise Exposure Measurements Regulations: Basis of 90dB(A) for 8hr a day. ISO(1999): Increase in SPL from 90 to 93dB(A) must reduce time of exposure from 8 to 4 hours OSHA: with every 5dB(A) increase, reduce exposure by half Occupational Safety and Health Administration

Noise Rating Curves (ISO R 1996) Level of Noise Annoyance NR78

Errors of the order of 6dB around 400Hz due to reflections

Sources: Vibration and Noise for Engineers, K Pujara Fundamentals of Acoustics, Kinsler and Frey Fundamentals of Noise and Vibration Analysis for Engineers, M Norton and D Karczub Introduction to Acoustics, R D Ford Measuring Sound, B&K Application Notes Sound Intensity, B&K Application Notes Basic Concepts of Sound, B&K Application Notes

TRANSFORMER NOISE CASE STUDY

SOURCES The primary source of acoustic noise generation in a transformer is the periodic mechanical deformation of the transformer core under the influence of fluctuating electromagnetic flux associated with these parts. The physical phenomena associated with this tonal noise generation can be classified as follows: vibration of the core core laminations strike against each other due to residual gaps between laminations

The material of a transformer core exhibits magnetostrictive properties. The vibration of the core is due to its magnetostrictive strain varying at twice the frequency of the alternating magnetic flux. The frequencies of the magnetic flux are equal to the power system supply frequency and its harmonics. When there are residual gaps between laminations of the core, the periodic magneto-motive force may cause the core laminations to strike against each other and produce noise. Also, the periodic mutual forces between the current-carrying coil windings can induce vibrations.

A core structure is a complicated stack of Si-Fe alloy laminations clamped together at suitable points. Clamping is essential to hold together the laminations. The clamping arrangement also influences the dynamic behaviour of a core. As laminations do not have good matching flat surfaces and as they are not clamped together over an entire surface area, hence residual gaps between the laminations are unavoidable. Magneto-motive forces acting across these air gaps could set relative transverse motions between the laminations also with clamped constraint points in place. Higher the core loss (eddy current loss, hysterisis, copper loss) greater the noise level. Figure: Core overlap region Noise level increases with increasing overlap length.

METHODS By changing the conventional grain-oriented (grade M4) material of core with any of high-permeability (Grade MOH) and laser-scribed (grade ZDKH) material can reduce noise 2-4db because higher-grade materials have lower magnetostriction. A method of controlling noise is to construct a wall with high sound absorbing bricks. The most effective way to reduce noise is varnishing or using adhesive material inside transformer tank (Viscoelastic materials) –Enclosing transformer inside an enclosure which uses two thin plates separated by viscous material. – The noise hits inner plate and energy is damped out by viscous material so that outer one does not vibrate.

This may change an efficiently radiating vibration shape into an ineffectively radiating shape resulting in a lower sound radiation ratio.

Active noise control (ANC):

Figure6: Configuration of the control simulation. Decentralized ANC can be implemented. In this transformer tank surface is divided into number of elements. For each element unit consist of micro phone located in front of loud speaker delivers error signal, this signal is fed to controller which drives loud speaker is attached. An experimentation of decentralized active noise control on power transformer is shown in figure 5 and Configuration of the control simulation is shown in figure 6. Figure 5: experimentation of decentralized active noise control on power transformer

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