Waves Special Topics in Physics 1
Waves Types of Waves: - longitudinal - transverse Longitudinal: Compression waves, e.g. sound Surface: Transverse: Attributes: Ocean Waves. Light, string etc. Speed, wavelength, frequency, period, amplitude, angular velocity, wavenumber...
Longitudinal Waves How does sound travel? This is what also happens with sound. There are regions of high and low compression. For a wave to propagate, there must be an interaction between the parts of the wave: e.g. push or pull. 3
Longitudinal Waves Fast: Or Slow Watch the red dots 4
Transverse Waves One eample is the wave on a string. It is transverse because the disturbance is perpendicular to the direction of the motion of wave. Compare this to the longitudinal wave where the disturbance is in the same direction as the wave motion. For a wave to propagate, there must be an interaction between the parts of the wave: e.g. push or pull. 5
Transverse Waves A string: Or in a material: 6
Surface Waves What is a surface wave? A typical wave in the ocean. A particle in the water will move in a circular or elliptical path as the wave passes. The size of the circle (or ellipse will decrease under water. For a wave to propagate, there must be an interaction between the parts of the wave: e.g. push or pull. 7
Surface Waves A miture of transverse and longitudinal waves The material still is not going anywhere! 8
Words Wavefront: The wavefront is the describes a point on the wave. It is used to describe the motion of the wave. 9
Attributes: Wavelength: m The wavelength is the distance between adjacent maima (or between adjacent minima The amplitude is the distance between the maimum of the disturbance and the equilibrium point. Just as with simple harmonic motion. 10
Attributes: Period: At a fied location along the wave, the maima will occur at fied intervals of time. This interval is referred to as the period: Frequency: f 1 T 1/ sec Hz The frequency is the inverse of the period. T sec 11
Attributes: Velocity: The speed of propagation of a wave front. Consider a maima, and the period: v T f What does this velocity depend on? 1
Solids: Stress and Strain What happens if we pull on a material? What do we call this?. Stretching? - this is actually a statement of the result. In Physics terms we apply a force And then there is a change: F L L F L L C10.13
Longitudinal Stress The amount of change will depend on the cross-sectional area. As a result we are interested in: F / A or the force per unit area. This is referred to as: Longitudinal Stress = As a result of the stress, the object will stretch. This is referred to as: Longitudinal Strain: Longitudinal Strain L L F A C10.14
Longitudinal Stress If we apply too much Stress (Force what will happen? The object will deform and then break. If there is not too much stress, and the stress is removed, the object will return to its initial state. This behaviour is called Elasticity It can be described as: Longitudinal Stress = (constant Longitudinal Strain Or: F A L constant L C10.15
Solids: Young s Molus The constant is referred to as: Young s Molus, or E Thus F L E A L E has units of: N / m N / m Rubber: 110 7 0.01 Copper: 1.310 11 130 Lead: 1.610 10 16 Gold: 7.810 10 78 Steel:.110 11 10 Diamond: 1.0510 1 1050 GPa C10.16
B Sound Waves How does sound propagate? First consider a solid pipe through which sound travels. A The volume of the pipe between and is: A If there is a disturbance that is passing through the pipe than there will be a displacement of the particles: s(, t Thus the location of the particles initially at move to: s(, t And similarly: s(, t 17
B Sound Waves The volume of the pipe between and is now: A Here we can note that:, (, ( t s t s A V The change in the volume is:, (, ( t s t s A A V A V, (, ( t s t s A, (, ( t s t s A t s t s L L V V, (, ( 0 18
B Sound Waves At this point we are ready to calculate two problems: 1 Sound through a fluid. Sound through a solid. V L s(, t s(, t V L 0 ds d For a solid: L L ds d and F A E L L Thus the force at is: F( EA ds d 19
General solution for a wave Proof (for F: The general solution is: y v t y 0 y v t y 0 y v t v t ( (, ( vt G vt F t y vt u u df v dt u df dt u df ( ( ( (, ( u F t y First take the first derivatives: u df d u df d u df ( ( ( 0 y v t 0
General solution for a wave Then take the second derivatives: d F( u dt d dt v df( u v d df( u dt v d df( u dt v d F( u d F( u d d d df( u d df( u d d df( u d d F( u Then we insert into the wave equation: F t v F v F u v F u 1
Wave Direction? Take a look at a point on the wave y. If we follow the wave, then the value will remain constant. If y is constant, then: y(, t Asin t k const t k const const And the velocity of the wave: t k d d const t v dt dt k k y(, t Asin t k v k And for:
Wave Power As we already discussed, in a wave, the particles are all oscillating. No particles are transferred. On the other hand the wave does transfer energy. Assume: y(, t Asin t k The disturbed particle will have a velocity of: v y dy(, t dt Acos The maimum velocity will be: And the maimum kinetic energy: t k vma A K ma 1 mv ma 1 m A 3
Wave Power (cont. For simple harmonic motion, the energy remains constant (kinetic + potential The mass of one wavelength is: So, the energy contained in one wavelength is: One wavelength will pass a point every T seconds, Or there will be f wavelengths per unit time. Thus the power is: P A v E K ma P 1 A E T Ef is in general true. m 1 A f 1 A v 4
Sound Waves There is a difference depending on if the material is a fluid or a solid Sound through a fluid: Where: v K K is the bulk molus (adiabatic for gases Sound through a solid: Where: v E E is Young s molus 5
Speed of Sound The speed of sound is the fastest when? 0 Gases v (m/s Hydrogen (0 C 186 Helium (0 C 97 Air (0 C 343 Air (0 C 331 Liquids at 5 C v (m/s Glycerol 1904 Sea water 1533 Water 1493 Mercury 1450 Kerosene 134 Methyl alcohol 1143 Carbon tetrachloride 96 Solids E, K v (m/s Diamond 1000 Pyre glass 5640 Iron 5130 Aluminum 5100 Brass 4700 Copper 3560 Gold 340 Lucite 680 Lead 13 Rubber 1600 v F K v S E 6
Intensity When we are interested in describing the strength of a sound or light wave, we refer to the intensity. I P A Power Area For a plane wave, the Intensity will remain constant. For a spherical wave (like sound, it will vary according to the surface area of a sphere: I P 4r This is in units of: Power at the source W / m cut steel: 9 10 W / m 7
Intensity (Decibel db For sound we usually use a unit called a decibel. This is a relative unit less scale: For sound: I 1 1 W / 10 m db 10log Based on the threshold of hearing 0dB I I 1 For eample: if I = 10 6 W/m, the power in db: P db = 10 log 10 6 W/m 10 1 W/m = 10 log 106 = 60dB 8
Intensity (Decibel db Or, for eample: if the power in db is: P db = 80dB, we can calculate the intensity of the sound wave I : 80dB = 10 log I 10 1 W/m 80 10 = log I 10 1 W/m 10 8 = I 10 1 W/m I = 10 4 W/m For light the decibel scale is used for power rather than intensity: And referred to as: P 10 3 1 W 1mW dbm 10log P P 1 9
Sound db-spl Jet engine at 3m 140 Threshold of pain 130 Rock concert 10 Accelerating motorcycle at 5m 110 Pneumatic hammer at m 100 Noisy factory 90 Vacuum cleaner 80 Busy traffic 70 Quiet restaurant 50 Residential area at night 40 Empty movie house 30 Rustling of leaves 0 Human breathing (at 3m 10 Threshold of hearing (good ears 0 30
Sound Level Dangers 3
Noise Inced Hearing Loss (NIHL 33
Hearing Loss 34
Weekly Sound Eposure 35