Homework #4 Reminder Chap. 6 Concept: 36 Problems 14, 18 Chap. 8 Concept: 8, 12, 30, 34 Problems 2, 10 Chapter 8: Wave Motion A wave is a sort of motion But unlike motion of particles A propagating disturbance The rope stays in one place However something is moving Due Wed. 10/6 Wave properties But what moves? 1) Speed is characteristic of the medium elastic properties and inertia (mass) density 2) obey the principle of superposition - two superposed disturbances add or subtract 3) transfer energy along the direction of propagation. http://www.kettering.edu/~drussell/demos/waves-intro/waves-intro.html Mechanical waves require Some source of disturbance A medium that can be disturbed Some physical connection between or mechanism though which adjacent portions of the medium influence each other Waves transport energy Waves can reflect Whenever a traveling wave reaches a boundary, some or all of the wave is reflected When it is reflected from a fixed end, the wave is inverted Waves can pass through each other Two pulses are traveling in opposite directions The net displacement when they overlap is the sum of the displacements of the pulses Note that the pulses are unchanged after the passing through each other 1
Continuous wave Can generate a wave that occupies all of the rope by continuing to shake the end up and down. Nee new terms to describe this continuous wave. Period, frequency, wavelength Kind of waves a traveling disturbance that transports energy Transverse - wiggling the rope at one end Longitudinal - scrunching a slinky Transverse Waves In a transverse wave, each element that is disturbed moves perpendicularly to the wave motion Longitudinal Waves In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave A longitudinal wave is also called a compression wave What are water waves? Water waves occur on the surface. They are a kind of transverse wave. Waveform A Picture of a Wave Just like the pulse, a continuous wave moves. The red curve is a snapshot of the wave at some instant in time The blue curve is later in time A is a crest of the wave B is a trough of the wave On Earth On the sun 2
Longitudinal Wave Represented on a graph A longitudinal wave can also be represented as a sine curve Compressions correspond to crests and stretches correspond to troughs Description of a Wave Amplitude is the maximum displacement of string above the equilibrium position Wavelength, λ, is the distance between two successive points that behave identically Period and frequency of a wave Period: time required to complete one cycle Unit = seconds Frequency = 1/Period = rate at which cycles are completed Units are cycles/sec = Hertz Frequency, wavelength, and velocity are related Period: Time required for source to emit one cycle Wavelength: spatial length of one cycle. One wavelength must be gone before the next one comes. Must move one wavelength ( λ ) in one Period ( T ). Velocity = Wavelength/Period Equation form Velocity = Wavelength / Period v = λ / T, or v = λf f = frequency = 1/T Periodic waves Shake one end of a string up and down with period T (frequency f=1/t). The height (up or down) is the amplitude. Peaks move at speed v so are separated by distance (wavelength) λ=vt = v/f. The wave can shake a fixed object with that frequency. 3
Examples The speed of sound in air is 340 m/s. A source period of 1 Hz=1/s produces a wavelength of λ=v/f= 340 m A string vibrating at frequency f= 340 Hz produces a wavelength λ=v/f = 1 m Wave quantities summary o Time of one COMPLETE up and down motion one period T = 1/f one wavelength in one period o Velocity of disturbance (wave or phase) velocity o Particles don t move with v (only up-and-down) or (back and forth) v = λf v depends only on properties of medium Speed of a Wave on a String The speed on a wave stretched under some tension, F F m v = where µ = µ L The speed depends only upon the properties of the medium through which the disturbance travels Producing a Sound Wave Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave A tuning fork will produce a pure musical note As the tines vibrate, they disturb the air near them As the tine swings to the right, it forces the air molecules near it closer together This produces a high density area in the air Area of compression Tine swings to left Area of rarefaction Sound from a Tuning Fork As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork A sinusoidal curve can be used to represent the longitudinal wave Crests correspond to compressions and troughs to Speed of Sound v = elastic property inertial property The speed of sound is higher in solids than in gases The molecules in a solid interact more strongly, elastic property larger The speed is slower in liquids than in solids Liquids are softer, elastic property smaller Speed of waves on a string v = F µ Tension Mass per unit length Fri. Oct 1 rarefactions Phy107 Lecture 11 4
Examples Speed of Sound in a Solid Rod The speed of sound in air is 340 m/s. A source period of 1 Hz=1/s produces a wavelength of L=v/f= 340 m A string vibrating at frequency f= 340 Hz produces a wavelength L=v/f = 1 m The speed depends on the rod s compressibility and inertial properties v = Y ρ Y is the Young s Modulus of the material The density of the material, ρ Speed of Sound in a Fluid Hearing In a liquid, the speed depends on the fluid s compressibility and inertia Listening to the radio v = B ρ B is the Bulk Modulus of the fluid The density of the fluid: ρ Real sounds Various Intensities of Sound Most sounds are not purely sinusoidal They have a frequency, and a wavelength, but the structure can be quite complicated. This structure (waveform) is part of what makes different sounds sound different. In addition, the way they turn on and off is quite important in recognizing a sound. Threshold of hearing Faintest sound most humans can hear About 1 x 10-12 W/m 2 Threshold of pain Loudest sound most humans can tolerate About 1 W/m 2 The ear is a very sensitive detector of sound waves 5
The decibel scale The sensation of loudness is logarithmic in the human hear The intensity level or the decibel level of the sound, β: I β = 10 log I o I o is the threshold of hearing: I 0 = 1.0 x 10-12 W/m 2 Threshold of hearing is 0 db Threshold of pain is 120 db Jet airplanes are about 150 db 6