Physics in Entertainment and the Arts

Transcription

1 Physics in Entertainment and the Arts Chapter VIII Control of Sound The sound characteristics (acoustics) of a room depend upon a great many complex factors room size/shape wall/floor/ceiling materials room contents (including people!) Some materials are extremely effective at absorbing sound Rooms lined with these materials are acoustically dead Sound does not reflect off the interior surfaces Anechoic Chambers In a normal room, sound reflects off all the interior surfaces The sound you hear is a superposition i of all the reflections and the direct path sound These rooms, called anechoic chambers, are useful in studying the acoustical properties of devices In a large room the sound takes awhile to die down due to echoes off the surfaces In a small room the sound dies off very quickly There are few if any echoes The time it takes for the amplitude of the sound in a room to decrease to one onethousandth of its original value is called the reverberation time Final amplitude = Initial amplitude/1000 The reverberation time for a gymnasium would be several seconds due to the large flat smooth walls, floor, and ceiling The reverberation time for this classroom would be only fractions of a second

2 The sound reflecting/absorbing properties of a room can be significantly affected by the shape of the interior surfaces Curved ceilings/walls can concentrate sound at certain locations An effect called focusing Source Receiver Focusing of Sound by a Curved Surface Not only the shape of the surfaces can have an effect so can the actual nature of the surface material Suppose we have a surface that has multiple repeating indentations a form of design to appeal to the viewer and make the surface stronger! Sound waves incident on the surface will reflect at different times since some have to travel a little farther A path length difference of 1 foot means Constructive interference for f = 1.1 khz, 2.2 khz, 3.3 khz, 4.4 khz, etc (n = 1) (n = 2) (n = 3) (n = 4) Destructive interference for f = 550 Hz, 1.65 khz, 2.75 khz, etc (n = 1/2) (n = 3/2) (n = 5/2) Same material, but with much narrower slits (of the same depth) The 1 inch spacing does not affect any waves with wavelength greater than 1 inch PLD = 12 inches = 1 foot Numerically: λ = 1 inch = feet v 1100 ft / s f = = = khz λ Any sound waves with f < 13.2 khz will not be able to penetrate this surface The surface will be flat as far as these waves are concerned In summary, waves are not significantly affected by obstacles in their paths which are small compared to their wavelengths Hence, small irregularities in surfaces affect high frequency (short wavelength) waves more than low frequency (long wavelength) waves Example #1: Bat sonar is high frequency (short wavelength) in order for them to see the small insects they eat

3 Wave affected greatly by bug Wave not affected greatly by bug Example #2: The holes in a microwave oven window are large to reflect the longer wavelength microwaves back into the oven but small enough to pass very short wavelength visible light That way you can see in without the microwaves leaking out! A system may have many different natural (resonant) frequencies Some or all of these frequencies may be excited at once such as a plucked or bowed stretched string Let s look at the simplest case of a stretched string with a small weight attached at the center small weight fixed endpoints (nodes) The natural vibrational frequency of this system depends upon the weight of the small weight the tension in the string This system is not very interesting since it only has 1 resonant vibrational frequency If we add a second evenly spaced weight we get a more interesting system: This system has two vibrational modes Note that the frequencies are not harmonics! Adding a third weight gets even more complicated: This system has three vibrational modes Once again, they are not harmonics If all parts of the string are vibrating at the same frequency as is the case with our three examples we say that the string is vibrating in a normal mode If we vibrate the string at one of its modes the entire string vibrates at only that mode and no others Suppose we vibrate the three weight string at a frequency which is not one of its vibrational modes In that case the string would vibrate using a combination of its three available modes The resulting motion would be difficult to draw, but can be easily represented on a graph called a vibration recipe

4 Relative Amplitu de Vibration Recipes This graph shows one possible combination of the vibrating string Vibrational Mode (in order of increasing frequency) Note that this resulting vibration is a mixture of normal modes 1 and 3, but no mode 2, with mode 1 being the dominant mode In this way we can graphically represent extremely complicated waveforms in an easy to understand format This technique is also useful if the vibration is 2-dimensional versus 1- dimensional This is a drawing of a square metal plate clamped at the center and set into vibration by rubbing it with a violin bow at the edge There is powder spread on the plate surface which tends to congregate at the nodes and antinodes of the vibrations Pictures of the various vibrational modes of a square metal plate Vibration Recipes None of these systems so far are harmonic systems The normal mode frequencies are not integer multiples of each other These systems would not be considered musical because of this Let s now look at some musical systems (with harmonic normal modes) String s Start with a stretched string and vibrate it at one of its natural resonant frequencies It will vibrate and produce a pure tone sound Vibration recipe of a pure tone nonmusical sound String s If we bow or pluck the string instead, it will vibrate at many harmonic frequencies and produce a very complex sound String s Plucking the string at its midpoint excites the fundamental frequency (which has an antinode at the midpoint) but not the 2 nd harmonic (which has a node at the midpoint) String s Plucked at 1/3 rd the distance from one end excites all harmonics but the 3 rd, 6 th, 9 th, and 12 th (all of which have nodes at that point) Vibration recipe of a complex musical sound L L L/

5 String s So we can control the sound the string produces by changing the way we pluck/bow the string and/or changing the location where we pluck/bow the string String s If we pluck the string near one of its ends we won t excite the fundamental frequency (which has a node there) but will excite many of the higher harmonics (which have antinodes there) The opposite is true if we pluck the string near its midpoint Summary: String s Pluck near the string ends get higher frequency harmonics (the treble ) Pluck near the middle get lower frequency harmonics (the bass ) String s String s String s Example An electric guitar Since there is no resonant cavity to generate sound such as in an acoustic guitar An electric guitar has at least two sets of pickups (expensive ones have more) one near the bottom bridge at the string ends to pickup the high frequency treble harmonics Guitar pickups treble pickups Electric transducers known as pickups are used to convert the vibrations of the strings into electrical signals one nearer the string midpoints to pickup the low frequency bass harmonics bass pickups String s Vibrational Modes Vibrational Modes When a string is plucked, the frequencies slowly die off as the plucked energy is dissipated by friction Consider a tuning fork struck sharply It will vibrate in several modes at once initially A tuning fork is not a harmonic system! Initially A few second later oscope traces The higher frequencies die off quicker than the lower ones This results in the sound quality changing as the seconds pass After several seconds, the higher frequency modes will die off leaving only the fundamental mode a pure tone sound Vibration Mode Vibration Mode

6 To reproduce an instrument s sound faithfully with high fidelity as it s called the instrument s vibration recipe must be determined This is done by a process known as Fourier Analysis Results of a Fourier Analysis of a trumpet s sound Trumpet Ditto for a clarinet Clarinet (in Low Register) And for an oboe Oboe (in Low Register) Given these vibration recipes, we can electronically reproduce these instrument s sounds by generating each harmonic frequency and then adding them together with the appropriate amplitude Phase Relationships The phase relationship between two waves while producing a wave which is visually different on an oscilloscope has no effect on the sound since our ears can t hear the difference so we don t have to worry about it for sound reproduction Phase Relationships As far as our ears are concerned both of these waves are identical: Wave Clipping and Distortion One other aspect of electronic reproduction of sound is sound modification by electronic distortion Distortion is the inability of the electronics to follow the vibration recipe exactly Wave Clipping and Distortion Example of electronic distortion A m p l i f i e r The distortion introduces higher frequency modes and harmonics into the sound which are not supposed to be there

7 Wave Clipping and Distortion s and System Response A system s response to excitation will be affected by the natural resonance frequencies of the system The harmonics which lie within the system s resonance response will be amplified at the expense of the other harmonics s and System Response The top graph is the applied excitation frequencies over the system s response (the dashed curve) The bottom graph is the combination of the two Note how the frequency within the response curve is amplified over its original s and System Response Another example The two highest frequencies are amplified due to resonance effects in the system