Chapter 14 Waves and Energy Transfer Quiz 14 Chapter 14 Objectives • Identify how waves transfer energy without transferring matter • Contrast transverse and longitudinal waves • Relate wave speed, wavelength, and frequency Chapter 14 Objectives • Relate a wave's speed to the medium in which the wave travels • Describe how waves are reflected and refracted at boundaries between media, and explain how waves diffract • Apply the principle of superposition to the phenomenon of interference Major Ideas Waves and types of waves Period and Simple harmonic motion Crests, troughs, amplitude, wavelength Frequency and Herz Waves A wiggle in space and time. Waves, like conduction, can transfer/transmit energy from one point to another without transporting any matter between two points. They transfer the energy by oscillation, by a vibration. Disclaimer: “in space” means larger area. A bell when struck will vibrate, but it for the most part, stays in the same space it was before. The sound it produces is a wave and exists over a large area of space Types of Waves Transverse waves and longitudinal waves. Transverse waves: the motion of the particles is perpendicular to the wave motion. Longitudinal waves: the motion of the particles is parallel to the wave motion. SHM The back and forth vibratory motion of a wave is called simple harmonic motion (or oscillatory motion). The simple harmonic motion follows a sin curve over time. Terms of Waves Period: How long it takes to go from crest to crest (back to start) Crests: The high points of a wave (compression in longitudinal) Troughs: The low points (rarefaction in longitudinal) Terms of Waves Midpoint: The “Home position,” the middle of the wave Amplitude: Distance from midpoint to crest (or trough) Wavelength: Length of wave, generally measured from one crest to another Review How often a vibration occurs is its frequency. It is however many back and forth divided by time (per second). If two vibrations happen in a second, it then has a 2 vibrations per second, or 2 hertz (Hz). Hertz is the unit of frequency. Radio Waves AM radio waves are broadcast in kilohertz (960 AM is 960 kHz) FM radio waves are broadcast in megahertz (so 100.7 FM is 100.7 MHz) Random Some Noisy Bugs fun info Bumblebees flap their wings with a frequency of 130 Hz Honeybees about 225 Hz Mosquitos about 600 Hz (or 0 Hz after you squash it) Questions The Sears building in Chicago sways at about 0.1 Hz. How many times per day does the Sears tower sway back and forth? How long does it take a bumble bee to flap their wings one time? The frequency of the wings is 130 Hz. Question How seconds does it take for the radio wave 98.5 FM to complete 200,000 periods/cycles? Owning the Air Radio stations purchase different frequencies to send out. Introduction of DTV is so that the radio waves can be used by other sources (police) In-between radio stations, the radio waves become mixed as your receiver is receiving two messages at the same frequency. Major Ideas Wave Speed and Temperature Dependence Factors influencing wave speed (inertia and restoring force) v f Warm Up A person is listening to the radio. The radio is receiving signals with a period of 9.93E-9s. Is the person listening to AM or FM? What is the station? The distance from crest to trough of a water wave is 0.35m, what is the wavelength? Introductory (Don’t Write) Most information you take in today will be via wave (sound and light (which comes to us through electromagnetic waves)). Energy is transferred through waves, but not matter. If you were to tie one a rope to a wall and give it a shake (like you would a hose), the wave moves through the medium (the rope), but the rope stays where it was (after being jiggled). If you drop a stone in a pond, the ripples produce move outward, but the water stays where it was (it goes up and comes down). When you talk, your voice produces a wave which goes through the room to the listener, but the air from your throat does not. Wave Speed Velocity (m/s) = wavelength (m) times frequency (1/s) v f Question What is the wavelength of the radio station 94.1 FM? The speed of an EM wave is 3E8 m/s. A ripple in a pond has a frequency of 0.20 seconds and wavelength of 0.12 m. What is the speed at which the wave travels outward? Wave Speed Factors Two major things which influence the speed of sound, the restoring force, and the measure of inertia. More restoring force makes wave speed faster More inertia makes waves slower. What is restoring force? It is a measure of how hard something is to compress, with the harder to compress the more restoring force. If molecules are packed tightly already (and therefore hard to compress), the energy can be transferred very quickly The matter doesn’t move, but the wave does. In order for the wave to move, it needs matter to move through. What is the measure of inertia? It is the density. As the energy is passed through, it is carried by the molecules. A molecule that is very heavy, given the same amount of energy as a molecule which is very light, will move slower through the propogation of the wave. Wave Speed Comparison Hydrogen Gas propagates waves at a speed of 1284 m/s. Mercury (l) propagates waves with a speed of 1450 m/s. Since mercury is 150,000 times more dense, shouldn’t its sound waves travel much slower? Explain. Wave Speed dependence on Temperature Temperature does have a slight effect on the speed of sound passing through air (molecules more energetic to begin with). The equation is v v0 T T0 Wave Speed and T Where T is in absolute temperature (Kelvin), V0 is wave speed initially. Normally you compare to 273 K (T0) which has a V0 of 331 m/s. Increasing Temperature does have its limits though for increasing wave speed. Too hot and the wave becomes incoherent. Question What is the speed of a sound wave at 50 C? Question You are at a concert, and the wave speed traveling through the air is 340 m/s. Two instruments are playing. Find the wavelength of the note they are playing Instrument FrequencyWavelength __________ 264 __________ m __________ 396 __________ m Major Ideas Interference, standing waves, and superposition Warm Up A horn near the beach emits a 440 Hz sound wave. (a) What is the wavelength of the sound in the air (T = 20 C)? (b) What is the wavelength of the sound in the water (Speed of water = 1520m/s)? Standing Waves, Nodes, Antinodes and Interference While matter can not exist in the same space and time as other matter (Two rocks can not exist in the same place), waves can and do (right now our bodies have bazillions of waves passing through them). If you drop two rocks in a pond, the waves can overlap and form an interference pattern. The wave effects are increased, decreased, or even neutralized. Types of Interference When a crest hits another crest, they add together and increase amplitude. This is called constructive interference. When a crest hits a trough, the waves are cancelled out, the crest “fills in” the trough. This is called Destructive interference. Out of Phase (180 degrees) In Phase Major Ideas Reflection, Refraction, and Diffraction Review How do crests and troughs line up with waves that are a) In phase? b) Out of phase? Explain what the Doppler effect is and how it works. Reflection Waves send energy in one direction (none backwards) as long as there is no change in medium (the path through which they travel). When a wave runs into a different medium (ie a wall) the medium changes and some of the energy may be reflected back. Refraction Not all of the energy of the wave is reflected when coming across a boundary (change in medium). The wave splits up: some reflects and some transmits (passes through new medium). The frequencies of both reflected and transmitted wave will be the same. However, the wave speed and wavelength may not be Refraction Frequency does not change Velocity and Wavelength do f v1 1 v2 2 Refraction The difference in speed causes the wave to refract, or change the angle at which it transmits through the material. The amount of refraction is based off the speed difference of the two waves sin 1 v1 sin 2 v2 Refraction The angles above are angle of incidence and angle of refraction and are measured between the direction of the wave and the normal. Normal: Perpendicular to surface Waves move faster in deep water Refraction Allows us to see pennies in the bottom of a cup with water from the side Keeps us from knowing exactly where the fish is under water Diffraction Diffraction is the spreading of a wave around an obstacle in its path. How much diffraction occurs depends on the wavelength of the wave and the size of the obstacle. How much diffraction In general: If the wavelength is small compared to the length/width of the obstacle, then very little diffraction will occur. (Light waves are very short, less than 1 micrometer so they don’t bend around much of anything) If the wavelength is of comparable size to the obstacle (or larger), then bending occurs easily. (Sound waves are about 1m in length and bend around corners easily). Diffraction When a wave passes through a gap, diffraction is greatest when the width of the opening is comparable to the wavelengths as well. Take note of how the gap produces a point source of a wave (like dropping a pebble in a pond) Following Slide Question A wave in deep water is traveling at 2.4 m/s. The wave direction is 30 degrees off of the normal when comparing the deep water to the shallow water. If the wave travels at 2.0 m/s in the shallow water, what is the angle of refraction that has occurred?