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Conceptual Physics Study Notes & Questions: Week 8—Vibrations (Chap. 14)

1) A vibration is a back and forth motion (p289). Now, moving any mass back and forth requires acceleration and a force to push or pull it. Energy is needed to get a vibration started—work has to be done on the mass.

2) The fact that a system wants to vibrate means a restoring force is also present. That is, work is done to move the mass from its equilibrium state (giving it potential energy), then a restoring force pulls it back toward its equilibrium state. In the case of pendulum-like motion (which occurs in some form or another in almost all physical systems), momentum and kinetic energy are built up by the restoring force acting on the mass—causing the system to shoot past equilibrium until an opposite-acting restoring force slows it down and pulls it once again back toward equilibrium. Once a vibration starts in a frictionless, elastic system, no energy is required to keep it vibrating—it is like an ideal pendulum (p290)—with a constant interchange between potential and kinetic energy.

3) A system that exhibits simple harmonic motion (p290) means that the time period of the vibration is constant, no matter what the initial size of displacement is. For example, in an ideal clock pendulum, the time period between its ticks will always be 1 second, no matter whether the pendulum is swing back and forth by 1 inch, 2 inches or 7 inches.

4) A vibration that travels is called a wave. (p291) Think of a water wave. It moves with a certain velocity (v), (p292) that is, it has speed and direction. The highest point of the wave is called its crest; the lowest point is called its trough. The distance between two adjacent crests or two adjacent troughs is called the wavelength (). The time (in seconds) it takes the wave (in a fixed spot) to change from crest to trough to crest again, is called its period. How many times this cycle occurs in one second is called the wave frequency (f), and its units are hertz (Hz; 1/sec). The wave equation is: v = f (p293). Wave amplitude is the distance the wave crests and troughs extend from equilibrium—so the total magnitude between the crest height and the trough depth equals twice the wave amplitude.

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5) A vibration holds energy. If the vibration occurs in an elastic or semi-elastic medium, the vibration propagates outward through medium, carrying energy with it. Traveling waves carry energy. Almost all waves need a medium in which to travel. The exception is light—light waves do not need a medium—they sort of create their own (more later…)

6) There are 2 types of waves:a) In a semi-rigid medium—like a solid—back and forth vibrations

can ripple forward through the matrix of atoms or molecules perpendicular to the back & forth motion. This is called a transverse wave—the vibration spreads out transverse to the direction of vibration. For example, the up & down wiggle of one atom is transferred via intermolecular forces to its neighboring atoms—this wiggling motion spreads left and right, even though the actual atomic motion is up & down. Certain types of seismic (earth) vibrations are transverse waves. Water waves and other types of surface waves are also transverse waves. Light is a transverse wave. Although transverse waves can travel on the surface interface of a liquid, they can not travel inside the liquid—the atoms are too loosely bound for the up & down motion to be transferred right and left to neighboring atoms via intermolecular attraction.

b) In a compressive or semi-compressive medium—which includes all states of matter—longitudinal waves (compression waves) can travel. In this case, the wave consists of local compression and rarefaction (“thinning out”) that occur along the same direction the wave is traveling. Sound is a longitudinal wave. So are certain types of seismic waves.

7) Waves superimpose on one another, that is their amplitudes combine to make the composite wave larger (constructive interference) or make the wave smaller (destructive interference). (p296)

8) Light waves can interfere with one another, especially when they are partially reflected off thin molecular membranes like soap bubbles or oil slicks. This type of interference pattern is wavelength (that is, color) dependent. What is iridescence? (p297)

9) Standing waves are essentially physically extended vibrations (p298). What are the nodes and anti-nodes of standing waves?

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10) The Doppler Effect occurs when a wave source is moving toward you or away from you—OR you are moving toward or away from the wave source. The waves reaching you (for example, sound waves coming from an ambulance) are shifted up in frequency as the source approaches, and they shift down in frequency as the source recedes (p299). How does Doppler radar detect tornadoes? (p300)

11) In the spread pattern of a wave dispersion (e.g. waves spreading across a pond) can be described by its wave fronts—that is—the continuous lines of wave crests. Wave fronts are perpendicular to the direction of wave travel.

12) In some circumstances, wave fronts pile up on top of one another, creating a shock wave—which produces a very intense vibrational jolt when it passes. What is an example of a shock wave (p301)?

13) Usually, waves interact only weakly with their host medium. Resonance occurs when a passing wave’s frequency corresponds to the natural vibrational frequency of its medium. In this case, the medium’s vibrations can build up very large amplitude swings. What can happen in cases of runaway resonant vibrations? (p303)

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Conceptual Physics Study Notes & Questions: Week 8—Sound (Chap. 15)

1) Sound is a longitudinal wave propagation in gas, or liquid, or solid, or plasma. The speed of sound in normal air is 344 m/sec, or about 1 mile in 5 seconds. (p313)

2) In thinner air (as in warm air), the compression wave that is sound, travels faster. So sound traveling along the boundary of warm and cool air will bend toward the thicker (cooler) air. The same is true in water—a fact submariners use to “hide” in the ocean from detection by surface ships. How do you think this occurs? (Figure 15-3, p313)

3) An echo is a reflected sound wave (p314). These reflections can occur off multiple surfaces, creating complex echo returns.

4) How does the ear detect sounds? (p316) How do bats hunt insects?

5) The shorter the wavelength of sound (that is, the higher the frequency), the more energy it contains. Ultrasound ( f > 20,000 Hz ) are very powerful and have many uses. Name some… (p318).

6) Sound intensity is the absolute measure of sound amplitude (p319), and it is measured on a logarithmic decibel scale (dB). Loudness, on the other hand, is the physiological sensation of sound intensity interpreted by the brain—which uses a relative scale. (p319).

7) Pitch is the musical word for sound frequency. When two sound waves have nearly the same frequency, they constructively and destructively interfere with one another, causing a beat pattern to be heard. (p321)

8) Harmonics (or overtones) are multiples of a given sound frequency. (p325) Every musical instrument produces a characteristic mix of harmonics that gives the instrument its distinctive sound or timbre.

9) Fourier analysis (p326) is a mathematical method for analyzing the frequency content of a complex sound.

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Conceptual Physics Study Notes & Questions: Week 8—Heat and Temperature (Chap. 11)

1) Temperature is a measure of thermal energy Temperature is a measure of the average molecular translational kinetic energy in a material. It has three widely used scales: Fahrenheit (F), Celcius (C), and Kelvin (K). (p228)

2) When the average molecular translational KE goes to zero, the temperature goes to absolute zero. This is related to the Ideal Gas Law (p217): PV / T= constant. When a fixed volume of gas is cooled, its pressure go down. Scientists extrapolated at what temperature the gas pressure would go to zero, and defined that as absolute zero.

3) Materials tend to expand when heated. The amount they expand varies from one material to another; each material has its own coefficient of thermal expansion. (p232)

4) Materials have internal energy, bound up in their molecular vibrations and intermolecular attractions. Their molecules also have translational KE, which is available to transfer to other materials. These forms of energy are collectively called thermal energy. The movement of thermal energy from one material to another is called heat. (p234)

5) Simple atoms simply bounce around—their thermal energy is all tied up in their translational KE. Large complicated molecules not only bounce around, they also have many ways their constituent atoms can vibrate relative to one another—their chemical bonds act like springs. These internal vibrations also contain KE, and make up a sizeable part of the internal energy of a material. When an object is heated, the introduced thermal energy gets distributed over all available vibrational modes of the molecules. Heat capacity is a measure of how much thermal energy a material can absorb; this measure varies from one material to another and it called the material’s specific heat (p235), and it tells us how much heat 1 gram of material can absorb before its temperature is raised one degree C.

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6) Heat can also disrupt the molecular attractions that keep solids solid and liquids liquid, causing a material to change from one state to another. The thermal energy needed to change 1 gram of material from one phase to another is called its latent heat. (p238) What is this thermal energy called for melting a solid? …for evaporating a liquid into gas?

7) Heat is transferred by three mechanisms:a) Conduction (p240) –heat transferred by direct contact; that is,

by passing KE vibrations from one atom to another like a bucket brigade.

b) Convection (p241) –heat transferred by molecular motion carrying hot material from one location to another.

c) Radiation (p244) –heat transferred by infrared radiation (IR).

8) Greenhouse Effect (p245): visible light gets absorbed by materials. This EM energy gets redistributed among the many vibrational modes of molecules and re-radiates as infrared radiation. Gasses or other materials (which are transparent to visible light) reabsorb the IR radiation—trapping it in the local environment. In other words, visible light gets converted to IR radiation (i.e. heat) and gets trapped.