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Review: Waves - I

Review: Waves - I. Quantum Mechanics:. Wave. Particle. Waves. Particle: a tiny concentration of matter, can transmit energy. Wave: broad distribution of energy, filling the space through which it travels. Types of Waves.

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Review: Waves - I

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  1. Review: Waves - I

  2. Quantum Mechanics: Wave Particle Waves Particle:a tiny concentration of matter, can transmit energy. Wave:broad distribution of energy, filling the space through which it travels.

  3. Types of Waves Types of waves: Mechanical Waves, Electromagnetic Waves, Matter Waves, Electron, Neutron, People, etc …… Transverse Waves: Displacement of medium Wave travel direction Longitudinal Waves: Displacement of medium||Wave travel direction

  4. Parameters of a Periodic Wave l:Wavelength, length of one complete wave form T: Period, time taken for one wavelength of wave to pass a fixed point v:Wave speed, with which the wave moves f:Frequency, number of periods per second l= vTv = l/T = lf

  5. When ∆x=l, 2p is added to the phase When ∆t=T, 2p is added to the phase k:wave number w:angular frequency Wave Function of Sinusoidal Waves y(x,t)= ymsin(kx-wt) ym:amplitude kx-wt :phase

  6. Wave SpeedHow fast does the wave form travel?

  7. Transverse Waves (String): v>0 y(x,t)= ymsin(kx-wt) v<0 y(x,t)= ymsin(kx+wt) Wave Speed How fast does the wave form travel? Pick a fixed displacement  a fixed phase kx-wt = constant

  8. Principle of Superposition Overlapping waves add to produce a resultant wave y’(x,t) = y1 (x,t) + y2 (x,t) Overlapping waves do not alter the travel of each other

  9. (2 ) f = n p 1 æ ö (2 ) f = n + p è ø 2 Interference Constructive: Destructive: n=0,1,2, ...

  10. Phasor Addition PHASOR:a vector with the amplitude ym of the wave and rotates around origin with w of the wave When the interfering waves have the same w PHASOR ADDITION INTERFERENCE Can deal with waves with different amplitudes

  11. Amplitude depends on position The wave does not travel Standing Waves Two sinusoidal waves with sameAMPLITUDE and WAVELENGTH traveling in OPPOSITE DIRECTIONS interfere to produce a standing wave

  12. NODES: points of zero amplitude ANTINODES: points of maximum (2ym) amplitude

  13. Standing Waves in a String TheBOUNDARY CONDITIONSdetermines how the wave is reflected. Fixed End: y = 0, a node at the end The reflected wave has an opposite sign Free End: an antinode at the end The reflected wave has the same sign

  14. k can only take these values OR where OR RESONANT FREQUENCIES: Case: Both Ends Fixed

  15. (b) Speed uz,min= wzm = 94 mm/s HRW 11E(5th ed.). (a) Write an expression describing a sinusoidal transverse wave traveling on a cord in the y direction with an angular wave number of 60 cm-1, a period of 0.20 s, and an amplitude of 3.0 mm. Take the transverse direction to be the z direction. (b) What is the maximum transverse speed of a point on the cord? (a) k = 60 cm-1, T=0.2 s, zm=3.0 mm z(y,t)=zmsin(ky-wt) w = 2p/T = 2p/0.2 s =10ps-1 z(y, t)=(3.0mm)sin[(60 cm-1)y -(10ps-1)t]

  16. (a) Phase (b) HRW 16P(5th ed.). A sinusoidal wave of frequency 500 Hz has a velocity of 350 m/s. (a) How far apart are two points that differ in phase by p/3 rad? (b) What is the phase difference between two displacements at a certain point at times 1.00 ms apart? y(x,t)= ymsin(kx-wt) f = 500Hz, v=350 mm/s

  17. For HRW 36E(5th ed.). Two identical traveling waves, moving in the same direction, are out of phase by p/2 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves?

  18. (a) ym2=7.0 mm ym h b f=0.8p q ym1=4.0 mm (b) The angle b is either 68˚ or 112˚. Choose 112˚, since b>90˚. HRW 41E(5th ed.). Two sinusoidal waves of the same wavelength travel in the same direction along a stretched string with amplitudes of 4.0 and 7.0 mm and phase constant of 0 and 0.8p rad, respectively. What are (a) the amplitude and (b) the phase constant of the resultant wave?

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