Wave - Tran Thi Ngoc Dung

Nội dung text: Wave - Tran Thi Ngoc Dung

1. WAVE Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. Contents 1. Mechanical waves Transverse, longitudinal, surface waves Speed of waves in solids, liquids, gases Energy of Mechanical waves 2. Sound Wave Intensity (dB), threshold of hearing , pain threshold Doppler effect
3. The essence of wave motion - the transfer of energy through space without the accompanying transfer of matter. Two mechanisms of energy tranfer depend on waves: - Mechanical waves - Electromagnetic radiation. All mechanical waves require (1)some source of disturbance, (2)a medium that can be disturbed, (3)and some physical mechanism through which elements of the medium can influence each other.
4. Transverse wave – Longitudinal wave – surface wave A longitudinal pulse along a stretched spring. The displacement of the coils is parallel to the direction of the propagation Wave that causes the elements of the disturbed medium to move The motion of water elements on the surface of perpendicular to the direction deep water in which a wave is propagating is a of propagation is called a combination of transverse and longitudinal transverse wave. displacements, with the result that elements at the surface move in nearly circular paths. Each element is displaced both horizontally and vertically from its equilibrium position
5. Characteristics of waves: -Wavelength -Frequency -Period -Amplitude (a) The wavelength  of a wave is the distance between adjacent crests or adjacent troughs. (b) The period T of a wave is the time interval required for the wave to travel one wavelength.
6. Speed of Sound -Depends on the property of the medium: BULK MODULUS B , and DENSITY  -Does not depend on the wave characteristics: Amplitude, frequency, period elastic property B v inertial property P Bulk Modulus : B (N / m2 ) V / V The ratio of the change in 1 V / V Compressibility :  pressure to the fractional B P volume compression is called the bulk modulus of the material. Bulk modulus B Density Sound speed (N/m2) (kg/m3) (m/s) Solid is difficult to be compressed, V/V small, Steel:160 x 10 ^9 7860 4512 B is large. Water: 2.2 x 10^9 1000 1483
7. Sound speed Gases v (m/s) elastic property B v Hydrogen (0°C) 1286 inertial property Helium (0°C) 972 Air (20°C) 343 Air (0°C) 331 Liquids at 25°C Bsolid Bliquid Bgas Glycerol 1904 Sea water 1533 solid liquid gas Water 1493 Mercury 1450 vsolid vliquid vgas Solids Diamond 12000 Pyrex glass 5640 Iron 5130 Aluminum 5100 Copper 3560 Gold 3240 Rubber 1600
8. Sound Speed in an ideal gas m PV nRT RT (1) Ideal gas law  RT  v The process of sound PV const (2)  travelling through an ideal gas can be expected to be adiabatic and therefore the pressure and volume obey Where: the relationship : adiabatic constant Differentiate PV  1dV V dP 0 (3) Gas constant: R=8.31 J/mol K dP : molecular mass of gas (g/mol) Bulk modulus B P | dV| / V T: absolute temperature (K) m P Density: Air :  =1.4, T=300K, V RT Sound speed B RT  =29 g/mol, R=8.31 J/mol K v  V= 347m/s The adiabatic assumption for sound waves means that the compressions associated with the sound wave happen so quickly that there is no opportunity for heat transfer in or out of the volume of air.
9. Speed of waves on a string F F: Tension (N) v  : the linear mass density (mass per unit length (kg/m) Example 15-1 The tension in a string is provided by hanging an object of mass M 3 kg at one end as shown in Figure 15-4. The length of the string is L 2.5 m and its mass is m 50 g. What is the speed of waves on the string? L Linear mass density m 50 10 3kg M  2 10 2(kg / m) Tension L 2.5m F Mg 3 9.8 29.4(N) 29.4 v 38.3m / s speed of wave on the 2 10 2 string
10. Frequency of Sound wave For Human being, Sonic frequencies: : 20Hz – 20 000Hz. Ultrasonic frequencies: > 20 000Hz Infrasonic frequencies: < 20Hz Ultrasound can be used in medical imaging, detection of defects in objects. Similar to light waves, sound waves can have Interference, Diffraction, Reflection phenomena , but different from light waves, sound wave is a longitudinal wave, it can not have polarization .
11. Mathematical Description of a Wave Wave function Let’s look at waves on a stretched string. Waves on a string are transverse; during wave motion a particle with equilibrium position x is displaced some distance y in the direction perpendicular to the x-axis. The value of y depends on which particle we are talking about (that is, y depends on x) and also on the time t when we look at it. Thus y is a function of both x and t y(x,t); We call y(x,t) the wave function that describes the wave y A wave moving in +x-direction wave function at O: y(0,t)=Acos (t) M z wave at M: y(x,t )=Acos ((t-x/v))=Acos(t-kx) k x O A wave moving in - x-direction wave function at O: y(0,t)=Acos (t) wave at M: y(x,t )=Acos ((t+x/v))=Acos(t+kx)
12. Graphing the wave function  2 2 k y= Acos(t-kx) v vT  (a ) we plot y as a function of x for (a ) we plot y as a function of t time t =0; y(x,t=0). for a point x=0: y(t=0,x) , the the curve shows the shape of the curve shows the displacement string at t =0. y of the particle at x=0 as a function of time.
13. Wave equation y Acos(t kx ) dy d2y Asin(t kx ); A2 cos(t kx ) dt dt2 dy d2y Ak sin(t kx ); Ak 2 cos(t kx ) dx dx2 2 2  k  v.T v d2y 2 2 dt v2 d2y k2 dx2 2y 1 2y Wave equation 0 x2 v2 t2
14. Wave Energy The essence of wave motion - the transfer of energy through space without the accompanying transfer of matter The displacement of the medium x element of mass dm = dV from the y Acos(t ) equilibrium position: v Its velocity: x vy Asin(t ) v 1 KE mv 2 Its KE: 2 y 1 x V A22 sin2 (t ) 2 v 1 2 2 KE VA  Average KE 4 1 In oscillation, average KE=average PE KE PE VA 22 4 Average Mechanical energy: 1 W KE PE VA 22 2 δW 1 w ρA2ω2 (J/m 3 ) Average energy density o δV 2
15. Vector Poynting: is a vector that has the magnitude equal to the energy that goes across a unit area perpendicular to the wave propagation direction during a unit time 2 U wo.v (W / m ) Energy that goes across area S during time interval dt is contained in the volume with cross section S, length vdt wo S dW wo (S vdt) Energy that goes across a unit area during a unit vdt time Energy Density dW 1 U wo.v w ρA2ω2 (J/m 3 ) Sdt o 2 U wo.v
16. Wave Intensity If a point source emits waves uniformly in all directions, the energy at a distance r from the source is distributed uniformly on a spherical surface of radius r and area A = 4πr2. If P is the power emitted by the source, The average power per unit area perpendicular to the direction of wave propagation is called the intensity I P I (W/m2 ) r 4 r 2 P the intensity equals the product of the average energy density and the wave speed v Point source dW 2 U wo.v (W/m ) Sdt U wo.v
17. Sound level - Threshold of hearing - Threshold of pain I Threshold of hearing: at 1000Hz: I = Io, L=0dB L(dB) 10log10 Threshold of pain: I = 1W/m2, L=120 dB Io 12 2 Io 10 W / m Io is the reference intensity, taken to be at the threshold of hearing I is the intensity in watts per square meter (W/m2) to which the sound level L corresponds, where L is measured in decibels (dB) Prolonged exposure to high sound levels may seriously damage the ear. Recent evidence suggests that“noise pollution” may be a contributing factor to high blood pressure, anxiety, and nervousness.
18. Auditory Canal Resonance The maximum sensitivity regions of human hearing can be modeled as closed tube resonances of the auditory canal. The observed peak at about 3700 Hz at body temperature corresponds to a tube length of 2.4 cm. The higher frequency sensitivity peak is at about 13 kHz which is somewhat above the calculated 3rd harmonic of a closed cylinder
19. The sensation of loudness depends on the frequency as well as the intensity of a sound. Figure is a plot of intensity level versus frequency for sounds of equal loudness to the human ear. (In this figure, the frequency is plotted on a logarithmic scale to display the wide range of frequencies from 20 Hz to 10 kHz.). We note from this figure that the human ear is most sensitive at about 4 kHz for all intensity levels.
20. Doppler Effect The change in frequency heard by an observer whenever there is relative motion between a source of sound waves and the observer is called the Doppler effect. We call the observed frequency is f’ , the source frequency f When they are moving toward each other, the observed frequency is greater than the source frequency: f’> f when they are moving away from each other, the observed frequency is less than the source frequency. : f’<f v: sound speed in the medium v vo vs: speed of source f' f ( ) v vs vo: speed of observer v Observer at rest , source approaches f ' f ( ) v vnguon v v Observer approaches, source at rest f ' f ( thu ) v
21. Source approaches, Observer approaches v v source Observer f' f ( o ) vs vo v vs Source approaches. Observer moves away v v source Observer f' f ( o ) v v vs s vo vs 20km/h , vthu 10km/h : f' f vs 20km/h , vthu 30km/h : f' f