Sound All sound begins with a vibrating object Ex. Vibrating tuning fork Vibrating prong sets molecules near it in motion

Transcription

1 Sound All sound begins with a vibrating object Ex. Vibrating tuning fork Vibrating prong sets molecules near it in motion As prong swings right, air molecules in front of the movement are forced closer together region of high molecular density and high air pressure called compression As prong swings to the left, molecules to the right of the prong spread apart and the density and air pressure is lower than normal this region called rarefaction As continues to vibrate, series of compressions and rarefaction form and spread away from each prong These compressions and rarefactions expand and spread out If tuning fork vibrating with SHM, so are air molecules Sound wave = longitudinal wave because particles vibrate parallel to direction of wave motion. Can be represented as a sine wave compressions = crests, rarefactions = troughs (y axis = density)

2 Sound wave is also called a pressure wave because it is a series of high and low pressure areas (compressions and rarefactions) Characteristics of sound waves Frequency Frequency = # of cycles per unit of time Audible sound waves (ones humans can hear) range from 20-20,000 Hz. f< 20 Hz = infrasonic waves (how elephants communicate) f> 20,000 Hz = ultrasonic waves (dogs can hear) we know as λ f therefore infrasonic waves = longer wavelengths than audible sound ultrasonic waves = shorter wavelengths than audible sound due to short wavelength have widespread medical applications used to produce images of objects inside the body short wavelengths easily reflect off of small objects to be able to see wavelength must be same size or smaller than the object, use 10 MHz device that 1500 m/s inside body so λ 1.5 mm device won t detect objects smaller than 1.5 mm Use to observe fetuses ultrasound sends out ultrasonic waves and then detects reflected sound waves which are converted to electrical signal which forms an image on fluorescent screen Dolphin echolocation works similarly dolphin sends out pulses of sound, which return as reflected sound waves. Dolphins can form an image of the object use high frequency waves b/c shorter wavelengths more effective for detecting smaller objects Frequency determines pitch Pitch = how high or low we perceive a sound to be As freq, pitch rises Frequencies are objective quantities and pitch is how a frequency is perceived Speed of sound depends on medium 1) State of matter Sound waves can travel through solids, liquids and gases. Speed of wave depends on how fast one particles can transfer its motion to another particle. Sound waves generally travel faster through solids than gases because particles are closer together in solid than in gas Exs. Air (0 o C) = 331 m/s Air (25 o C) = 346 m/s Helium gas (0 o C) = 972 m/s Methyl alcohol 25 o C = 1140 m/s Aluminum (solid) = 5100 m/s 2) temperature of medium as temp rises, particles of gas collide more frequently, thus sound wave travels faster at higher temp than low temp In liquids and solids, particles are close enough together that temp doesn t affect as much.

3 Sound waves propagate in three dimensions When musician plays trumpet in center of room, can hear sound all over room because sound waves spread out in all directions Represent spherical waves in 2 dimensions with a series of circles surrounding the source. Circles represent the centers of compressions called wave fronts Because each wave front corresponds to the center of a compression, the distance between adjacent wave fronts is equal to 1 wavelength The radial lines perpendicular to wave fronts = rays, which indicate the direction of the wave motion Doppler Effect: (show simulation PHET???) If stand on street while someone drives by honking horn you notice the pitch of the horn changes Pitch is higher as object producing sound moves towards you Pitch is lower as object moves away from you We said earlier that pitch depends on frequency but the frequency of car horn doesn t change so what causes change in pitch? Have to look at relative motion between moving car and stationary observer Relative motion affects the way wave fronts of the sound waves produced by the car s horn are perceived by the observer. As car moves towards, wave fronts reach observer much more often than if car was stationary frequency heard by observer is greater than source frequency therefore higher pitch

4 As car moves away, wave fronts reach observer less often than if car was stationary frequency hears by observer is less than source frequency therefore hear lower pitch This frequency shift is known as the Doppler effect (named after Austrian physicist Christian Doppler early 1800s) Doppler effect happens with all types of waves and can also occur between 2 moving objects police radar to monitor car speeds, a computer compares the frequency of radar waves emitted with those reflected from a moving car and then uses this comparison to calculate the speed of the car [WS #1-4] Sound Intensity When a piano key is struck, hammer inside the piano strikes a wire, which vibrates causes soundboard to vibrate, which exerts force on air molecules around it, causing air molecules to move B/c force is exerted through displacement of soundboard, the soundboard does work on the air and therefore the kinetic energy of the soundboard is converted into kinetic energy, which is why vibration of soundboard gradually dies out As sound waves travel, energy is transferred from air molecule to air molecule Rate at which energy is transferred through a unit area is intensity of wave We learned earlier that power is the rate of energy transfer so intensity can be described in terms of power Intensity = P/area If we are looking at a spherical wave in which energy travels equally in all directions, then power is distributed over a spherical surface (area = 4πr 2 ), assuming no absorption in the medium Intensity = P/4πr 2 Intensity = W/m 2 P = power (W) r = distance from the source (m) intensity of sound wave is inversely related to distance from source squared this is b/c same amount of energy is spread over a larger area

5 Intensity and frequency determine what sounds are audible Humans hear frequencies from 20 Hz Hz Intensity is also factor in determining audible sounds (Figure 13-10) To hear low frequencies or high frequencies have to have more intensity Threshold of hearing (softest sound heard by humans) is around 1000 Hz and 1 x W/m 2 (changes in pressure due to compressions and rarefactions are about three ten-billionths of atmospheric pressure) Loudest sounds humans can tolerate (threshold of pain) is 1 W/m 2 sounds with greater intensities can produce pain when hearing Exposure to sounds above the threshold of pain can produce immediate damage to the ear Relative intensity is measured in decibels Remember frequency determines pitch Intensity determines loudness (volume) but they are not directly proportional Relative intensity relating intensity of a given sound wave to the intensity of threshold of hearing corresponds to human perceptions of loudness also referred to as decibel level because relative intensity is measured in decibels (db) The decibel is a dimensionless unit because it relate one intensity to another Conversion of Intensity to decibel level Intensity (W/m 2 ) Decibel level (db) Examples 1 x Threshold of hearing 1 x Rustling leaves 1 x Quiet whisper 1 x Whisper 1 x Mosquito buzzing 1 x Normal conversation 1 x Air conditioning at 6 m 1 x Vacuum cleaner 1 x Busy traffic, alarm clock 1 x Lawn mower 1 x Subway, power motor 1 x Auto horn at 1 m 1 x Threshold of pain 1 x Thunderclap, machine gun 1 x Nearby jet airplane When intensity is multiplied by 10, 10 db added to the decibel level A difference in 10 db means sound is approximately twice as loud Since volume doubles each time decibel level increases by 10, sounds at the threshold of pain are 4096 times as loud as sounds at the threshold of hearing Forced vibrations and resonance When have isolated guitar string held taut and you pluck it almost no sound is heard If place same string on guitar and pluck it, the intensity of the sound increases dramatically Why? Because of forced vibration Ex. Of forced vibration set of pendulums suspended from a beam and bound by loose rubber band (Fig 13-11) if one pendulum set in motion, its vibrations are transferred by the rubber band to the other pendulums, which also begin vibrating

6 Back to guitar example when pluck string forces bridge of guitar to vibrate and the bridge transfers the vibrations to the guitar body these forced vibrations are called sympathetic vibrations The guitar body enables the strings vibrations to be transferred to the air much more quickly because the body has larger area than the strings Because of this, the intensity of the sound is increased and the strings vibrations die out faster than they would if not attached to the guitar s body (Sum up: the guitar body allows the energy to be more efficiently transferred from strings to air and that increases the intensity of the sound) In electric guitar string vibrations are translated into electrical impulses, which can then be amplified as much as desired Vibration at natural frequency produces resonance We know freq of a pendulum depends on string length therefore every pendulum will vibrate at a certain frequency known as natural frequency In earlier example with pendulums - #1 & 3 have same natural freq while 2 & 4 have different natural frequencies If only #1 is set in motion 2 & 4 will only vibrate slightly but #3 will oscillate with a much larger amplitude because its natural frequency matches the freq of pendulum that was initially set in to motion System is in resonance Energy will be transferred from one pendulum to another, so #1 will decrease amplitude while #3 will increase amplitude (Show resonance boxes and tuning forks) Example of structural resonance is when the Tacoma Narrows bridge (in 1940) was set in motion by wind

7 High winds set up standing waves in the bridge causing the bridge to oscillate at one of its natural frequencies. Amplitude of vibrations increased until the bridge collapsed. (Show video from United Streaming Physical Science: Structures Video Segments, Suspension Bridge need segment from 1:29-3:10) in 1989 near Oakland California, during an earthquake, part of an upper deck of a freeway collapsed due to the fact that the earthquake waves had a freq of 1.5 Hz, close to the natural freq of that section of the freeway our ear The human ear has three parts outer, middle, inner Sounds waves travel through the outer ear to the eardrum, which vibrates with the sound waves and transfers the vibrations to 3 small bones (hammer, anvil, stirrup), which then transfer the vibrations to the inner ear, which contains nail-shaped tube, the cochlea Different regions of the cochlea have different natural frequencies and sound waves create impulses in different nerve fibers. The impulses are sent to the brain, which interprets them [WS #5-14] Harmonics Standing waves on a vibrating string - When one end of string is attached and other end is moved back and forth with regular motion - Produces waves of certain frequency, wavelength, and amplitude traveling down string - Waves reach fixed end and are reflected back - If at right frequencies produce standing wave which is a wave pattern that occurs when 2 waves of same frequency, wavelength and amplitude travel in opposite directions and interfere -> alternating regions of constructive and destructive interference 1 st harmonic: 2 nodes and 1 antinode (draw example) Node = where cancel/destructive interference, no motion occurs

8 Antinode = largest amplitudes 2 nd harmonic: 3 nodes and 2 antinodes (draw example) 1 wavelength = 2 antinodes (if look at individual waves 1 crest & 1 trough) To determine what wavelengths will produce standing wave patterns- have to be at a frequency where both ends act as nodes for standing wave to be produced. If 4 meters of string: 1 st harmonic is ½ λ therefore a full wavelength = 8 m 2 nd harmonic is 1λ therefore full wavelength = 4 m 3 rd harmonic is 3/2 λ so 1 wavelength = 2/3(4) = 2.67 m The vibration on a string of a musical instrument usually consist of many standing waves together at same time (each w/ different wavelength and freq) even single pitches can consist of multiple frequencies The simplest vibration, 1 st harmonic, consists of just one antinode. The wavelength to produce this 1 st harmonic is = 2L Remember v = λf so f = v/λ Substitute in and get f = v/2l known as fundamental frequency the lowest possible frequency of a standing wave Harmonics are integral multiples of the fundamental freq For 2 nd harmonic, λ = L so f = v/l (it is twice as much) 3 rd harmonic, f = 3 times as much as fundamental freq This pattern of frequencies form a harmonic series Harmonic series of standing waves on a vibrating string: f n = n v/2l n = 1,2,3,4. f = frequency (Hz) n = harmonic number v = speed of wave (m/s) L = length of vibrating string (m) When guitar player presses down on string, that point becomes a node and only a portion of the string vibrates therefore a single string can be used to create a variety of fundamental frequencies Standing waves in an air column Standing waves can be set up in a tube of air (i.e. inside a trumpet, saxophone or pipes of organ) Some waves travel down the tube, other are reflected back and travel in opposite direction therefore creating standing waves Occur in most woodwinds and brass instruments Both ends open If both ends of pipe are open, the air molecules at the end of the pipe have complete freedom of motion and so an antinode can exist If both ends open, then both ends can be antinodes Entire harmonic series is present in a pipe with both ends open

9 Harmonic series of a pipe open at both ends: f n = n v/2l n = 1,2,3,4. L = length of vibrating air column Can change fundamental freq by changing length of vibrating column of air One end of pipe is closed When one end of pipe is closed, movement of air molecules at this end is restricted, making that end a node and he other an antinode Only odd harmonics are present in pipe with one end closed f n = n v/4l n = 1,3,5,. Exs of instruments w/ one end closed trumpet (person s mouth) clarinet & saxophone (reed) Harmonics account for sound quality (timbre) In music, the mixture of harmonics that produces the characteristic sound of an instrument is referred to as the spectrum of sound, which results in a response in the listener called sound quality (timbre) Timbre = the quality of a steady musical sound that is the result of a mixture of harmonics present at different intensities Intensity of each harmonic varies within instruments depending on freq, amplitude of vibration and many other factors Fundamental frequency determines pitch

10 Beats When we have 2 waves with slightly different frequencies that interfere interference patter causes listener to hear an alternation between loudness and softness. This variation is called a beat If have 2 tuning forks of different frequencies the waves produced start exactly opposite of each other creating destructive interference and no sound is produced they are said to be out of phase After a few more cycles, the crests will occur at the same time producing constructive interference and a louder sound is produced they are said to be in phase After a few more cycles will be out of phase again and no sound will be produced (demo with CPO speakers) Can calculate the number of beats per second by looking at the difference in frequency between the two sounds [WS #15-19]