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

Physics 1B03summer-Lecture 10 Day of Wrath Tuesday June 16 9:30 am – 11:30 am CNH MC Questions, Cumulative

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

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

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

Physics 1B03summer-Lecture 10 The mass dm vibrates in simple harmonic motion. Its maximum kinetic energy is dK max = ½(dm)v max 2 = ½(dm)(ωA) 2 dE = ½(dm) ω 2 A 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: To get the energy per unit length (or energy ‘density’), replace the mass dm with the mass per unit length  :

Physics 1B03summer-Lecture 10 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 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 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: a)the speed of the wave b)the speed of particles on the wave at any time c)the wavelength d)the frequency e)the power transmitted to the wave

Physics 1B03summer-Lecture 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? A)2mm B)4mm C)16 mm

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

Physics 1B03summer-Lecture 10 How would the intensity depend on distance from the source for: 1)waves spreading out equally in all directions in space? (This is called an“isotropic” source, or a source of “spherical waves”.) 2)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? Question

Physics 1B03summer-Lecture min rest

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

Physics 1B03summer-Lecture 10 -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). Fluids

Physics 1B03summer-Lecture 10 Density,  (“rho”), is mass per unit volume (kg/m 3 ). Specific Gravity (“SG”) is the ratio: (density of substance)/(density of water), which is a pure number (no units). Density Substance  SG  water 1000 kg/m 3 1 mercury kg/m air 1.29 kg/m helium 0.18 kg/m

Physics 1B03summer-Lecture 10 P  force per unit area unit: 1 N/m 2 = 1 pascal (Pa) Also, 1 atmosphere (atm) = kPa Pressure 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 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 Example: Example: How hard do you need to push to lift a cement truck (weight W = 200 kN)? F 1 = ? piston, radius 5mm piston, radius 100mm w

Physics 1B03summer-Lecture 10 Pressure variation with depth h P1P1 P2P2 Pressure increases with depth, by an amount P 2 – P 1  gh (if  and g are uniform). Proof: Consider forces on a cylinder of fluid

Physics 1B03summer-Lecture 10 “Gauge Pressure” : pressure difference between a fluid and the surrounding atmosphere. It is equal to P 2 –P 1. 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 Example At 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 Example What is the difference in air pressure between the floor and the ceiling?

Physics 1B03summer-Lecture 10 Example What 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?