Today’s Lecture…

1. Today’s Lecture… … will start at 10:30am (and end at regular time) Physics 1B03summer-Lecture 10

2. Day of Wrath Tuesday June 169:30 am – 11:30 amCNH-104 30 MC Questions, Cumulative Physics 1B03summer-Lecture 10

3. Wave Motion • Energy and power in sinusoidal waves Physics 1B03summer-Lecture 10

4. Energy in Waves • as waves propagate through a medium, they transport energyeg: ship moving up and down on a lakeeg: feeling sound waves at a rock concert • hence, we can talk about energy and the ‘rate of energy transfer’ Physics 1B03summer-Lecture 10

5. Energy and Power A stretched rope has energy/unit length: ds dm dx For small A and large l, we can ignore the difference between “ds”, “dx” : dm = μ dx (μ= mass/unit length) Physics 1B03summer-Lecture 10

6. The mass dm vibrates in simple harmonic motion. Its maximum kinetic energy is dKmax = ½(dm)vmax2 = ½(dm)(ωA)2 The average kinetic energy is half this maximum value, but there is also an equal amount of potential energy in the wave. The total energy (kinetic plus potential) is therefore: dE = ½(dm) ω 2A2 To get the energy per unit length (or energy ‘density’), replace the mass dm with the mass per unit length m: Physics 1B03summer-Lecture 10

7. Power: Energy travels at the wave speed v, So waves on a string, Both the energy density and the power transmitted are proportional to the square of the amplitude. This is a general property of sinusoidal waves. Physics 1B03summer-Lecture 10

8. Example A string for which μ=5.0x10-2 kg/m is under tension of 80.0 N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60Hz and with an amplitude of 6.0 cm ? Physics 1B03summer-Lecture 10

9. Example A sinusoidal wave on a string is described by the equation: y(x,t) = (0.15m)sin(0.80x-50t) where x is in meters and t in seconds. If μ=12.0g/m, determine: • the speed of the wave • the speed of particles on the wave at any time • the wavelength • the frequency • the power transmitted to the wave Physics 1B03summer-Lecture 10

10. Quiz The sound waves from your 100-watt stereo causes windows across the street to vibrate with an amplitude of 1 mm. If you use a 400-watt amplifier, what sort of amplitude can you get from the windows? • 2mm • 4mm • 16 mm Physics 1B03summer-Lecture 10

11. detectors (areaA) source Intensity I= Power per unit area Unit: W / m2 • (the area is measured perpendicular to the wave velocity) Intensity ~ (amplitude)2 Physics 1B03summer-Lecture 10

12. Question • How would the intensity depend on distance from the source for: • waves spreading out equally in all directions in space? (This is called an“isotropic” source, or a source of “spherical waves”.) • Waves spreading out on a two-dimensional surface, e.g., circular ripples from a stone dropped into water? How would the amplitude depend on distance? Physics 1B03summer-Lecture 10

13. 10 min rest Physics 1B03summer-Lecture 10

14. Fluid Mechanics and Dynamics • Pressure • Pascal’s Law • Buoyancy • Bernoulli’s Equation (Fluid Dynamics) Physics 1B03summer-Lecture 10

15. Fluids • Includes liquids and gases. No resistance to “shear” (changes in shape), in equilibrium. • To describe mechanics of a continous fluid (instead of a discrete object), we use density, pressure instead of mass and force. • Dynamics is approached from an energy perspective (Bernoulli’s equation—next lecture) . Physics 1B03summer-Lecture 10

16. Density Density, r (“rho”), is mass per unit volume (kg/m3). Specific Gravity (“SG”) is the ratio: (density of substance)/(density of water), which is a pure number (no units). Substance r SG water 1000 kg/m3 1 mercury 13600 kg/m3 13.6 air 1.29 kg/m3 0.00129 helium 0.18 kg/m3 0.00018 Physics 1B03summer-Lecture 10

17. Pressure P  force per unit area unit: 1 N/m2= 1 pascal (Pa) Also, 1 atmosphere (atm) = 101.3 kPa Pressure is a scalar property of the fluid; the force is always exerted perpendicular to the surface in contact with the fluid. Forces exerted by the fluid Physics 1B03summer-Lecture 10

18. Pascal’s Law: Pressure in an enclosed fluid in equilibrium is the same everywhere, except for differences due to gravity. Or, pressure changes are transmitted throughout a fluid in equilibrium without loss; there is no static friction in fluids. push here Pressure increases here as well Physics 1B03summer-Lecture 10

19. Example: How hard do you need to push to lift a cement truck (weight W = 200 kN)? w piston, radius 100mm F1 = ? piston, radius 5mm Physics 1B03summer-Lecture 10

20. Pressure variation with depth Pressure increases with depth, by an amount P2 – P1= r gh (if r and g are uniform). P1 h Proof: Consider forces on a cylinder of fluid P2 Physics 1B03summer-Lecture 10

21. “Gauge Pressure” : pressure difference between a fluid and the surrounding atmosphere. It is equal to P2–P1. Example: a tire gauge measures gauge pressure, and reads zero when the air inside the tire is at atmospheric pressure. “Absolute Pressure” is the pressure compared to vacuum. Zero absolute pressure means a vacuum. Example: the pressure on the surface of the earth. Physics 1B03summer-Lecture 10

22. ExampleAt what depth in water is the pressure 1 atm higher than the pressure on the surface? That is, where is P=2atms ? Physics 1B03summer-Lecture 10

23. ExampleWhat is the difference in air pressure between the floor and the ceiling? Physics 1B03summer-Lecture 10

24. ExampleWhat is the total mass of air directly above a 1-metre square, from ground level all the way to outer space? Approximately how thick is the atmosphere, assuming (incorrectly) that the air density is uniform? Physics 1B03summer-Lecture 10