SOUND A vibrating object, such as your voice box, stereo speakers, guitar strings, etc., creates longitudinal waves in the medium around it. When these waves cause our ear drums to vibrate, we “hear” sounds. vibrations ! Sound is caused by vibrations !

Sonic Spectrum The frequency range over which longitudinal waves occur. The frequency range over which longitudinal waves occur. That part of the sonic spectrum that the human ear is sensitive to is called the aural range (a.k.a. sounds) That part of the sonic spectrum that the human ear is sensitive to is called the aural range (a.k.a. sounds) 20 Hz – 20,000 Hz (wavelength range: 17mm – 17m) 20 Hz – 20,000 Hz (wavelength range: 17mm – 17m) Ultrasonic: frequencies above 20,000 Hz Ultrasonic: frequencies above 20,000 Hz Infrasonic: frequencies below 20 Hz Infrasonic: frequencies below 20 Hz

Upper frequency limit is determined by the medium. Upper frequency limit is determined by the medium. If the wavelength of the sound is small compared to the inter-particle spacing the wave will not be transmitted. If the wavelength of the sound is small compared to the inter-particle spacing the wave will not be transmitted. Small wavelength means high frequency. Small wavelength means high frequency. Gases – around 10 9 Hz at ordinary temperature and pressure. Gases – around 10 9 Hz at ordinary temperature and pressure. Solids/liquids – higher than 10 9 Hz due to closer spacing of particles. Solids/liquids – higher than 10 9 Hz due to closer spacing of particles. Sonic Spectrum

Sound Waves Wave energy is passed through the particles of the medium as a periodic, longitudinal wave. Wave energy is passed through the particles of the medium as a periodic, longitudinal wave. Remember: the wave travels, not the medium! Remember: the wave travels, not the medium! The particles alternately experience compression and rarefaction. The particles alternately experience compression and rarefaction.

Speed of Sound Factors affecting the speed of sound Factors affecting the speed of sound Temperature: the hotter the medium the faster the speed of sound. Temperature: the hotter the medium the faster the speed of sound. Air: v sound = m/s +.6T (T is in degrees C) Air: v sound = m/s +.6T (T is in degrees C) Density: the denser the medium the faster the speed of sound. Density: the denser the medium the faster the speed of sound. 0 0 C: m/s 0 0 C: m/s Steel: 5200 m/s Steel: 5200 m/s

Try one! A ship sounds its fog horn to find out how far away an iceberg is. If the captain hears the echo 6 sec after sounding the horn, how many meters away is the iceberg? (assume T = 6 0 F) A ship sounds its fog horn to find out how far away an iceberg is. If the captain hears the echo 6 sec after sounding the horn, how many meters away is the iceberg? (assume T = 6 0 F) Given: t = 6.0 s, T = 6 0 F Given: t = 6.0 s, T = 6 0 F 6 0 F to Celsius: C = (5/9)(F – 32) = C 6 0 F to Celsius: C = (5/9)(F – 32) = C Find the speed of sound: v sound = m/s Find the speed of sound: v sound = m/s Calculate the distance. Remember, the sound has to travel twice the distance between them! Calculate the distance. Remember, the sound has to travel twice the distance between them! 2d = vt so d = ((322.9m/s)*(6s))/2 = 969m 2d = vt so d = ((322.9m/s)*(6s))/2 = 969m

Sound Barrier Sound waves spread out from their source in spherical shells, similar to ripples in a pond. Sound waves spread out from their source in spherical shells, similar to ripples in a pond. If the source is moving close to the speed of sound, the waves begin to pile up in front of it. If the source is moving close to the speed of sound, the waves begin to pile up in front of it.

Sound Barrier When the source moves at the speed of sound each new crest is created on top of the last one causing constructive interference When the source moves at the speed of sound each new crest is created on top of the last one causing constructive interference This creates an area of high pressure in front of the source called the “sound barrier.” This creates an area of high pressure in front of the source called the “sound barrier.”

Super Sonic Finally, when moving faster than the speed of sound, the source outruns the wave crests it creates. Finally, when moving faster than the speed of sound, the source outruns the wave crests it creates. The V pattern created by the successive wave crests is called a “shock wave,” with the source ahead of it. The V pattern created by the successive wave crests is called a “shock wave,” with the source ahead of it. This shock wave is the “sonic boom” we hear when something goes by at supersonic speed. This shock wave is the “sonic boom” we hear when something goes by at supersonic speed.

Properties of Sound Pitch (frequency) Pitch (frequency) High pitch (high frequency): shorter wavelength sounds such as a siren or a flute. High pitch (high frequency): shorter wavelength sounds such as a siren or a flute. Low pitch (low frequency): longer wavelength sounds such as a sub-woofer or a fog horn. Low pitch (low frequency): longer wavelength sounds such as a sub-woofer or a fog horn. Pitch can also be described with musical notes. Pitch can also be described with musical notes. Pitch (frequency) does not change when a sound wave passes from one medium to another. Pitch (frequency) does not change when a sound wave passes from one medium to another. Normal speech range; 1000 – 5000 Hz Normal speech range; 1000 – 5000 Hz

Properties of Sound Intensity (loudness) Intensity (loudness) A measure of the amount of sound energy that passes through a given area over a given time A measure of the amount of sound energy that passes through a given area over a given time I = P/A = Watts/cm 2 I = P/A = Watts/cm 2 Power is determined by the source, but the area increases with the square of the distance from the source. Power is determined by the source, but the area increases with the square of the distance from the source. Intensity is inversely proportional to the square of the distance from the source Intensity is inversely proportional to the square of the distance from the source A sound heard from 100m away is ¼ as intense when heard from 200m away. A sound heard from 100m away is ¼ as intense when heard from 200m away. Intensity is also a measure of the amplitude of the sound wave. Intensity is also a measure of the amplitude of the sound wave.

Intensity (continued) Intensity (continued) The decibel scale relates sound intensity to our perception of how loud sounds are. The decibel scale relates sound intensity to our perception of how loud sounds are. Units: decibels (dB) Units: decibels (dB) β = 10log(I/I o ) β = 10log(I/I o ) I is the intensity of the sound heard I is the intensity of the sound heard I o is the intensity of a sound at the threshold of hearing I o = 1.00x W/m 2 I o is the intensity of a sound at the threshold of hearing I o = 1.00x W/m 2 β = 0 dB is the threshold of hearing. β = 0 dB is the threshold of hearing. β = 110 dB is considered the threshold of pain. β = 110 dB is considered the threshold of pain. However, sounds below 110 dB can still cause hearing loss. However, sounds below 110 dB can still cause hearing loss.

Try it! The intensity of a sound is found to be 1x W/cm 2. What is the sound level? The intensity of a sound is found to be 1x W/cm 2. What is the sound level? Given: I = 1x W/cm 2 Given: I = 1x W/cm 2 Convert I o to W/cm 2, I o = 1x W/cm 2 Convert I o to W/cm 2, I o = 1x W/cm 2 β = 10log[( 1x W/cm 2 )/(1x W/cm 2 )] β = 10log[( 1x W/cm 2 )/(1x W/cm 2 )] = 20 dB = 20 dB How much would the sound level change if the intensity was doubled? How much would the sound level change if the intensity was doubled? β would increase 3 dB. β would increase 3 dB.

Doppler Effect The change in frequency of a sound due to the relative motion between the source and listener The change in frequency of a sound due to the relative motion between the source and listener

Doppler Effect A decreasing distance between the source and observer will cause a higher pitch to be heard. A decreasing distance between the source and observer will cause a higher pitch to be heard. f o = frequency heard by observer f s = frequency of the source v = speed of sound v o = speed of the observer v s = speed of the source

Doppler Effect An increasing distance between the source and observer will cause a lower pitch to be heard. f o = frequency heard by observer f s = frequency of the source v = speed of sound v o = speed of the observer v s = speed of the source

Try it! A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren sounding at a frequency of 2,500 Hz. What frequency does the driver hear as the police car approaches? A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren sounding at a frequency of 2,500 Hz. What frequency does the driver hear as the police car approaches? Given: f s = 2,500 Hz, v = 343 m/s, v s = 40 m/s, v l = 25 m/s Given: f s = 2,500 Hz, v = 343 m/s, v s = 40 m/s, v l = 25 m/s The cars are getting closer so The cars are getting closer so

Doppler Effect (Light) A similar effect, but the equation is slightly different A similar effect, but the equation is slightly different f o = frequency seen by observer f o = frequency seen by observer f s = frequency of source f s = frequency of source c = speed of light c = speed of light v = relative speed between v = relative speed between observer and source observer and source

More Properties of Sound Reflection Reflection Refraction Refraction Interference Interference Need 2 waves Need 2 waves same frequency same frequency in phase in phase When the waves travel to the same point, the difference in their path lengths determines what type of interference occurs When the waves travel to the same point, the difference in their path lengths determines what type of interference occurs

1D Interference If L 2 – L 1 = n(½ ) (for n = 1,2,3…) then there will be total destructive interference If L 2 – L 1 = n(½ ) (for n = 1,2,3…) then there will be total destructive interference If L 2 – L 1 = m (for m =1,2,3…) then there will be total constructive interference If L 2 – L 1 = m (for m =1,2,3…) then there will be total constructive interference L1L1 L2L2

2D Interference As with 1D As with 1D  L = n(½ ) results in total destructive interference  L = n(½ ) results in total destructive interference  L = m results in total constructive interference  L = m results in total constructive interference You have to rely more on the path lengths than visual cues for 2D You have to rely more on the path lengths than visual cues for 2D

Beats When two tones are heard at the same time they interfere with each other causing a pulsing sound called beats. When two tones are heard at the same time they interfere with each other causing a pulsing sound called beats. The frequency of the beat pattern is the difference between the frequencies of the two tones. The frequency of the beat pattern is the difference between the frequencies of the two tones. f b = f 1 - f 2 f b = f 1 - f 2

Let’s try it! Jane holds two slightly different tuning forks next to her ear. What is the beat frequency she hears if one tuning fork vibrates at 440Hz and the other at 436Hz? Jane holds two slightly different tuning forks next to her ear. What is the beat frequency she hears if one tuning fork vibrates at 440Hz and the other at 436Hz? f b = 440Hz – 436Hz = 4Hz f b = 440Hz – 436Hz = 4Hz

Forced Vibration Forced Vibration a vibrating object is touched to a second object a vibrating object is touched to a second object the second object begins to vibrate at the same frequency the second object begins to vibrate at the same frequency Resonance Resonance a vibration caused in a medium due to a disturbance that occurs at the medium’s natural frequency a vibration caused in a medium due to a disturbance that occurs at the medium’s natural frequency the natural frequency is the frequency of oscillation in an object that will produce a standing wave the natural frequency is the frequency of oscillation in an object that will produce a standing wave unrestricted, the amplitude of the vibrations will continue to increase unrestricted, the amplitude of the vibrations will continue to increase Shake it Up

The Sound of Music Musical instruments are designed to resonate at one or more natural frequencies Musical instruments are designed to resonate at one or more natural frequencies The strings on a string instrument have a base frequency based on its length and tension (remember last chapter?), but they can produce other notes by putting pressure on the fret board effectively shortening the string The strings on a string instrument have a base frequency based on its length and tension (remember last chapter?), but they can produce other notes by putting pressure on the fret board effectively shortening the string Wind and brass instruments create resonance patterns in the “pipe-like” body Wind and brass instruments create resonance patterns in the “pipe-like” body

Resonance in Pipes There are two kinds of pipes to consider There are two kinds of pipes to consider Open pipes – open at both ends Open pipes – open at both ends a standing wave is created in the pipe such that there is an antinode at each end a standing wave is created in the pipe such that there is an antinode at each end the wavelength of the standing wave depends on the length of the pipe the wavelength of the standing wave depends on the length of the pipe for n = 1,2,3,…

Resonance in Pipes Closed pipes – closed at one end open at the other Closed pipes – closed at one end open at the other a standing wave is created in the pipe such that there is a node at the closed end and an antinode at the open end a standing wave is created in the pipe such that there is a node at the closed end and an antinode at the open end the wavelength of the standing wave depends on the length of the pipe the wavelength of the standing wave depends on the length of the pipe for n = 1,3,5

Wind and Brass Instruments Wind instruments act like an open pipe Wind instruments act like an open pipe Brass instruments act like closed pipes Brass instruments act like closed pipes

Let’s try it! In an unheated 10 0 C room, a 25cm pipe is producing its 3 rd harmonic. If the pipe is open at both ends, what is the frequency of the tone heard? In an unheated 10 0 C room, a 25cm pipe is producing its 3 rd harmonic. If the pipe is open at both ends, what is the frequency of the tone heard? first you find the speed of sound in the room v = (10) = 337.5m/s then you use the open pipe equation for n = 3 f = 3(337.5/(2x0.25m)) = 2025Hz