Physics in Entertainment and the Arts Chapter IV The Fine Arts Spectra; Some Second Looks at Waves Spectra of Continuous Waves A wave s spectrum is the range of frequencies the waves cover For sound the range of frequencies the ear can hear For light the range of frequencies the eye can see The human ear: 20 Hz f 20 khz 55 ft λ 0.055 ft The ear can hear frequencies over three orders of magnitude a factor of a thousand! 20,000 Hz/20 Hz = 1000 = 10 3 Current electronic devices that can do this are really expensive! Sound frequencies below 20 Hz are called infrasonic These are not heard but can sometimes be sensed as vibrations Sound frequencies above 20 khz are called ultrasonic Some animals can hear these, but not humans Ultrasonic Uses Auto-focus camera Ultrasonic cleaner Pregnancy ultrasound Since the wavelength and frequency of a wave are related v = λf The size of the sound maker or detector is approximately the same as the wavelength For example: The average human ear size is ~1.5 in = 0.13 ft If λ = 0.13 ft, then f = 8,500 Hz f = 1100 ft/s / 0.13 ft = 8,500 Hz This frequency is approximately in the middle of the range of human hearing! The human ear appears to be just the correct size to hear the average human voice It s almost as if it were planned that way Human vocal cords produce frequencies also in the range of human hearing More about stringed noise-makers later
Another example: Dolphin sounds cover a frequency range 1 khz 120 khz The speed of sound in seawater is ~4900 ft/s Yields wavelengths of 4.9 ft λ 0.49 in These wavelengths span the range of sizes of fish the dolphin might eat of other dolphins they may communicate with Sound Waves Sound waves can travel through any molecular medium except a vacuum (an absence of medium) Gases and liquids sound waves are longitudinal Solids sound waves can be longitudinal or transverse Sound Waves in Gases and Liquids Air molecules vibrate back and forth longitudinally Sound Waves in Gases and Liquids Sound Waves in Solids Light is a visible electromagnetic wave More about what this means later Focus on only one molecule it s only moving back and forth, not to the right! http://www.kettering.edu/~drussell/demos/waves/wavemotion.html Transverse Guitar string waves creating longitudinal sound waves http://journals.aol.com/darkfflames/sciencestuff/entries/2007/03/07/gitar-string-sound-waves/607 All electromagnetic waves travel at the speed of light (c) 186,000 miles/sec 300,000,000 meters/sec 670,000,000 miles/hr ~900,000 times faster than sound in air! Compare light waves and sound waves in terms of speed Example Shine a laser from the stage of a concert next to a speaker outputting music How long does it take both waves to reach the back of the stadium? Assume a distance to the back of the stadium 200 yards = 600 feet Sound wave at v = 1100 ft/s Time to travel 600 ft = 600 ft / 1100 ft/s t = 0.55 seconds Light wave at c = 980,000,000 ft/s Time to travel 600 ft = 600 ft / 980,000,000 ft/s t = 0.0000006 seconds = 0.6 µs six tenths of a millionth of a second! This time is essentially instantaneous as far as your eyes and ears are concerned You see the laser about ½ a second before you hear the sound
Let s try a longer distance example Suppose you see a bolt of lightning strike a tree on a hill 5 miles away (26,000 ft) Travel time for the light t = 5 miles / 186,000 miles/s = 0.000027 s = 27 µs Travel time for the thunder t = 26,000 ft / 1100 ft/s = 24 s So while you see the lightning almost instantaneously It takes almost half a minute to hear the associated thunder! Rule of thumb for lightning strikes 5 seconds = 1 mile away electrical signal direct sound rebroadcast sound The electrical signal goes from the microphone to the rebroadcast speaker at nearly the speed of light Close enough for government work This is nearly instantaneous as far as the audience is concerned The direct sound path is much longer than the rebroadcast sound path This means that, if not corrected, the audience hears the sound from the speaker before the sound arrives from the stage! The sound from the stage arrives delayed with respect to the speaker This delay is not much maybe 0.1 s for a typical auditorium But can be extremely annoying and confusing to the audience Ever watch a movie where the sound and the picture were out of sync? This problem is easily corrected by taking into account the differences in speeds between electrical and sound waves Just introduce a 0.1 s electrical l time delay in the signal to the rebroadcast speaker Then the sound from the stage and the speaker will arrive at the audience at the same times! This correction is actually more elaborate than it sounds Since the speed of sound in air changes with air temperature As the room heats up from body heat the time delay must be adjusted during the performance to compensate An even more subtle correction is also added Humans perceive sound as coming from Humans perceive sound as coming from the first source we hear even if the first source is weaker (quieter) As it would be coming from the farther away stage We ll discuss why this is later
To ensure the audience perceives the sound as coming from the stage rather than the speaker An additional ~0.02 s delay in the electrical signal is added so that the sound from the stage arrives oh-so slightly ahead of the speaker sound This fools the audience into perceiving the sound as coming from the stage rather than the speaker(s) And you thought being a stage hand wouldn t require a knowledge of science! Hah!! Humans (and other animals) perceive light of different colors All light waves travel at the same speed c = 186,000 miles/sec The different colors are due to different wavelengths and frequencies of the electromagnetic waves This table summarizes the visible light spectrum Remember: c = f λ and 1 nanometer = 10-9 meters Color Frequency Wavelength Hertz millionths of inches meters nanometers red 4.6 x 10 14 26 6.5 x 10-7 650 green 6.0 x 10 14 20 5.0 x 10-7 500 violet 7.5 x 10 14 16 4.0 x 10-7 400 Note for Humans: Range of hearing 20 Hz 20 khz A factor of 1000 from bottom to top Range of sight 4.6 x 10 14 Hz 7.5 x 10 14 Hz A factor of only 1.6 from bottom to top Human ears have a very wide range of frequencies which can be perceived Human eyes have a very narrow range of frequencies which can be perceived Our sense of sight is not nearly as effective as our sense of hearing Note: 4.6 x 10 14 = 460,000,000,000,000 and 6.5 x 10-7 = 0.00000065 The Electromagnetic Spectrum Visible light is only a very small portion of the electromagnetic spectrum The full spectrum runs from radio waves at the largest wavelengths hence lowest frequencies, lowest energies to gamma rays at the smallest wavelengths hence highest frequencies, highest energies The Electromagnetic Spectrum visible light!! http://www.latrobe.edu.au/spacescience/swunit/html/students/studunit1.htm Uses of Radio waves FM/AM radio cell phones television television microwave ovens Wi-Fi RFID tags GPS
Triangulation FCC Style GPS satellite Period ~ 24 hours Triangulation GPS Style Uses of Ground tracks Infrared waves TV remotes thermal imagers thermometers heat lamps heat-seeking missiles! remote temperature sensing Uses of Visible light lasers illumination television Ultraviolet light tanning black lights dental amalgams disinfectants Uses of X-rays and Gamma rays noninvasive imaging cancer treatments Because of their high penetrating power x-rays and gamma rays can kill cells and hence humans! Electromagnetic waves are different from sound or mechanical waves Speed All electromagnetic waves travel at the same speed c = 186,000 miles/sec Not true for other waves
Type of wave All electromagnetic waves are transverse waves always! Sound waves are longitudinal in gases and liquids Sound waves can be longitudinal and transverse in solids Medium Electromagnetic waves can travel in any medium and in pure vacuum All other waves require a medium They cannot travel in a vacuum! In space, no-one can hear you scream! Wave production Sound or mechanical waves require a disturbance in the medium Electromagnetic waves don t need a medium! So what is waving? What is being disturbed? Electromagnetic waves consist of rapidly varying electric and magnetic fields which are mutually perpendicular transverse waves These rapidly varying fields are produced by oscillating charged particles E = electric field B = magnetic field An oscillating voltage applied to a long wire will oscillate the metal s electrons The oscillating electrons produce oscillating electric and magnetic fields in tandem which radiate outward from the wire This is the electromagnetic wave! The reverse process occurs on the receiving end The electromagnetic wave induces oscillations of the metal s electrons in the receiving wire The electron s oscillations produce an oscillating voltage which is amplified to drive a speaker! Another example of wavelength vs size The average television frequency is ~500 MHz If f = 500 MHz, then λ = 2 ft λ = 186,000 mi/s / 500 MHz = 0.0003700037 mi = 2 ft This wavelength is approximately the length of most TV receiving antenna elements we ll refine this more in the next chapter