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Daily Challenge, 10/26WHAT IS SOUND?
Earlier, we saw how waves on a Slinky can cancel each other, add together to make
one big wave, pass through each other, or reflect off a boundary.
CAN SOUND WAVES DO ALL THAT?
SONIC SPECTRUMthe frequency range over which
mechanical longitudinal waves occur
the lower limit is undefined (earthquake P wave frequencies ~ 0.001 Hz, wavelengths that are kilometers long)
the upper limit is well defined must be greater than inter-particle spacing for propagation to occur
So what are the upper limits?
at ordinary temperature & pressure, upper range of sonic frequency ~ 109 Hz in gaseous medium
upper range of sonic frequency is higher in solids and liquids because particles are closer together
SOUNDa.k.a. audio spectrum
the portion of sonic spectrum to which the human ear is sensitive (20 Hz – 20,000 Hz)
ultrasonic waves – longitudinal waves at frequencies > sound
infrasonic waves – longitudinal waves at frequencies < sound
How are sound waves produced?
through a VIBRATION which produces compressions and rarefactions in a medium
capable of propagating these waves
Air can propagate sound waves, more dense air is better transmitter than less dense air.
Liquids are excellent sound transmitters of sound waves.
SOME solids are good transmitters of sound waves.
Practice ProblemThe speed of sound in air is 331.5 m/s at 0°C and increases with temperature at
(0.6 m/s ) / °CLight travels at about 300,000,000 m/s.
If lightning strikes one mile away from you, what will be the lag time between seeing the lightning and hearing the thunder?
Daily Challenge, 10/28The speed of sound in air is 331.5 m/s at 0°C &
increases with temperature at (0.6 m/s )/°C
You see a helicopter pass directly overhead. Two seconds later you hear the sound of the engines. If the air temperature is 23°C, how
high was the helicopter flying?
FREQUENCYPITCH is the characteristic of sound that depends on the fundamental frequency received by the human ear.
NOISE is unpleasant sound, random mix of frequencies
MUSIC is pleasant soundoctaves have a frequency ratio of 2:1major chords have frequency ratios of 4:5:6:8
BEATS
BEATS are amplitude pulsations through time that result from the interference of two close frequencies.
Number of Beats per second = frequency difference in Hz
Sound IntensityIntensity = power / area
(Power is measured in Watts, area in m2)Intensity is the time rate at which sound energy flows through a unit area normal to the direction of wave propagation.
depends on wave amplitudemeasured with an acoustical instrument
We detect intensity as the LOUDNESS of a sound, but the perception of loudness may vary from ear to ear.
Relative Sound Intensity, is the intensity compared to the threshold of hearing on a logarithmic scale due to the great range of human hearing
d = 10 * log (I/Io) d is the relative intensity in decibelsI is the intensity of the soundIo is the intensity of the threshold of
hearing (assumed to be 10-12 W/m2)
Type of Sound Relative Intensity (d) hearing threshold 0
whisper 10-20
conversation 60-70
rock concert 110
pain threshold 120-130
jet engine 150
The relative intensity of the sound of a jet engine is 165 dB at a distance of 4.65 meters
from the engine. How much sound energy does the engine produce in one minute?
Practice Problem
Daily Challenge, 10/29
How is it that we can recognize different people’s voices, even when they sing the same note?
FUNDAMENTAL TONES
If a string vibrates as a whole (as a single unit) it produces its lowest frequency, which is called the FUNDAMENTAL tone.
A string itself disturbs very little air, so a SOUNDING BOARD is used to make it louder (increasing intensity).
HARMONICS
Strings (and other things) may vibrate in segments in addition to vibrating as an entire unit
HARMONICS are frequencies that are whole number multiples of the fundamental. The fundamental is called the first harmonic, twice the frequency is the second harmonic, etc.
Sound quality or TIMBRE depends on the number of harmonics produced and their relative intensities.
FORCED VIBRATIONS
FORCED VIBRATIONS occur when an object in contact with a vibrating object begins to vibrate.
SYMPATHETIC VIBRATIONS a.k.a. RESONANCE
RESONANCEoccurs when a sound wave causes an object to vibrate at its natural frequency
For a closed tube… f = v / (4L + 0.4d)only ODD harmonics are resonant frequencies
For an open tube… f = v / (2L + 0.8d)ALL harmonics are resonant frequencies
f = frequency of fundamentalv = velocity of sound in airL = length of tubed = inside diameter of tube
The Doppler EffectIf a sound source and/or listener are moving with respect to each other, the pitch of the sound the listener hears is changed.
Listener hears higher pitch as they move together, lower pitch as they move apart.
Will it matter whether the sound source is moving toward the listener or the listener is moving toward the sound?
YES!
The Doppler Effectgetting closer together getting further apart
Moving SourcefLF = fs * v / (v – vs) fLB = fs * v / (v + vs)
Moving ListenerfLF = fs * (v + vLC) / v fLB = fs * (v – vLO) / v
fLF = frequency heard by listener in front of sourcefLB = frequency heard by listener behind sourcefs = frequency of sound created by sourcev = velocity of sound in given mediumvs = velocity of the sourcevLC = closing velocity of the listenervLO = opening velocity of the listener
Applications of the Doppler Effect
weather monitoring (Doppler radar)
speed measurements (radar & laser guns)
Red Shift Big Bang Theory
Practice ProblemThe frequency of a particular fire alarm is 3500 Hz.
If the alarm is on a fire station and you are driving toward it at 25 m/s, what pitch do you hear?
If the alarm is on a fire truck, and the truck is driving toward your stationary position at 25 m/s, what pitch do you hear?
Daily Challenge, 10/30A physics student blows across the top of a graduated cylinder that is
23.0 cm tall and 4.00 cm in diameter. If the temperature in the
room is 21.5°C, what is the frequency of the sound produced?
LAWS OF STRINGS
Law of lengths: f/f = l/lthe frequency of a string is inversely proportional to its length if all other factors are constant (if your shorten the string, you raise the pitch)
Law of diameters: f/f = d/dthe frequency of a string is inversely proportional to its diameter if all other factors are constant (smaller diameter strings have higher frequencies, and therefore higher pitches, than larger diameter strings)
LAWS OF STRINGS (continued)
Law of tensions: f/f = F/F the frequency of a string is directly proportional to the square root of the tension on the string if all other factors are constant (when you tighten a string, you raise the pitch)
Law of densities: f/f = D/D the frequency of a string is inversely proportional to the square root of its density if all other factors are constant (the more dense a string, the lower the frequency)
Practice ProblemThe frequencies of two notes in a chord
played on a guitar have a ratio of 3:2. If the tension on the first string is 285N, what is the tension on the second string assuming
all other factors are equal?
Daily Challenge, 11/2
If I have a guitar string in which I double the tension and cut the vibrating length in half, what will
happen to the frequency produced by the string?
(Give a quantitative answer.)
Daily Challenge, 11/3Write down three possible scientific questions you could investigate in a lab studying some aspect of sound.
