Physics 2 - Lecture 2: Waves - Huynh Quang Linh

Nội dung text: Physics 2 - Lecture 2: Waves - Huynh Quang Linh

1. WAVE Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. 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.
3. 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.
4. 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
5. 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
6. 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)
7. 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
8. 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
9. 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.
10. 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
11. 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