Physics 2101 Section 3 Apr 14th Announcements: Quiz Friday Midterm #4, April Midterm #4,

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1 Physics 2101 Section 3 Apr 14 th Announcements: Quiz Friday Midterm #4, April 28 th Final: May 11 th-7:30am Class Website: 6 pm Make up Final: May 15 th -7:30am 3/

2 Chap. 16 Waves Waves and particle Vibration waves - Sound - medium vibrates - Surface ocean waves - no net water is displaced - Mechanical waves - Newton s equations with medium - Electro-magnetic waves - NO MEDIUM light (photons) WAVES Pulse single wave Periodic wave sinusoidal waves Particle Displacement Velocity Acceleration

3 Oscillation vs Wave How do you describe the motion? How many variables do you need?

4 Traveling Waves A Pulse: A pulse can be sent along a spring it travels to the right ihtover time Repeating the Pulse: Generates a periodic traveling wave If it reflects off of the other (fixed) end correctly it becomes a Standing Wave it looks like the wave is standing still

5 Transverse vs Longitudinal Waves Transverse: Displacement of particle is perpendicular to the direction of wave propagation Longitudinal: Displacement (vibration) of particles is along same direction as motion of wave Sound (fluids ) Ocean O currents top vs bottom Traveling Waves they travel from one point to another Nodes move Standing Waves they look like they re standing still Nodes do not move

6 Transverse Waves In a transverse wave the motion of the particles of the medium is perpendicular to the direction of the wave s travel

7 Longitudinal Waves A longitudinal pulse travels along the medium but does not involve the transport of matter just energy Here are periodic longitudinal waves pick a single particle and follow its motion as the wave goes by

8 A Wave on the Water A water wave is a combination of a longitudinal and a transverse wave notice how the blue dots make a circular motion:

9 Description of transverse traveling wave Displacement (y) versus position (x) t = 0 y(x,0) = y max sin kx ( ) k = 2π λ Spatially Periodic ( repeats ) : kλ = 2π t = δ Temporally Periodic ( repeats ) : ωτ = 2π t = 2δ t = 3δ t = 4δ y(0,t), ) = y sin ωt ω = 2π max ( ) T Displacement versus time does not show shape

10 Description of transverse wave To describe a wave (particle) on a string, the transverse displacement (y) depends on both the position (x) along the string and the time (t) Displacement Y versus position X Displacement Y versus time t Spatially Periodic ( it repeats ) Temporally Periodic ( it repeats ) vt = λ v = λ T = fλ f = 1 T

11 Description of traveling wave: mathematical k = 2π λ ω = 2π T phase : kx ± ωt kx ωt kx + ωt Wave traveling in + x direction Wave traveling in x direction What is the velocity at which the wave crests move?

12 Wave speed Velocity at which crests move = wave velocity or phase velocity phase : kx ωt = const. k dx ω = 0 dt v wave = dx dt = ω k = λ T = λf A wave crest travels a distance of one wavelength, λ, in one period, T

13 Wave speed Velocity at which crests move = wave velocity or phase velocity v wave = dx = ω = λ dt k T = λf A wave crest travels a distance of one wavelength, λ, in one period, T Velocity of particle ( ) ( ) y(x,t) = y m sin kx ωt v t (x,t) = ωy m cos kx ωt v t (x,t) max = ωy m

14 Wavelengths of Radio Stations Waves like radio, light, x rays etc. are part of the electromagnetic spectrum. They travel with a velocity: v = c= = What is the wavelength of talk radio WJBO am 1150? speed of light / m s What is the wavelength of KLSU fm 91.1? f =1150 khz = Hz = Hz λ = c = m /s f /s = 261 m f = 91.1 MHz = Hz = Hz λ = c = m /s f /s = 3.29 m

15 Problems Sample problem 16 y(x,t) = sin( 72.1x 2.72t) A wave traveling along a string is described by: in which the numerical constants are in SI units ( m, 72.1 rad/m, and 2.72 rad/s). a) Which direction are the waves traveling? b) What is the amplitude of the waves? Positive x direction y max = m = 3.27 mm c) What is the wavelength? k = 72.1 rad/m λ= m = 87.1 mm d) What is the period? e) What is the frequency? ω= 2.72 rad/s Τ= 2.31 s Τ = 2.31 s f = Hz f) What is the velocity of the wave (v w )? v w = ω / k = λf =38 mm/s g) What is the displacement y at x = 22.5 cm and t=18.9 s? make sure your calculator is in radians y = 1.92 mm h) What is u, (or v t ) the transverse velocity, at x = 22.5 cm and t=18.9 s? u= ωy m cos(kx ωt) i) What is a t, the transverse acceleration, at x = 22.5 cm and t=18.9 s? a t = ω 2 y(x,t)

16 Problems (a) write an equation describing a sinusoidal transverse wave traveling on a cord in the +x direction with a wavelength of 10 cm, a frequency of 400 Hz, and an amplitude of 2.0 cm. k = 2π 2π rad = λ 0.10 m ( ) = 62.8 rad /m ω = 2π T = 2πf = 2π rad 400 1/s ( ) = 2513 rad /s [ ] y(x,t) = ( 0.02 m)sin ( 62.8 rad /m)x ( 2513 rad /s)t (b) What is the maximum speed of a point on the cord ( ) m u ω 1 max = ωy max = 2513 s ( ) = 50.3 m /s (c) What is the speed of the wave? 1 v wave = λ T = ω k = 2513 s = 40 m /s m