Sound, Wavefronts Wavefronts join points in phase Linear wavefronts.
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Transcript of Sound, Wavefronts Wavefronts join points in phase Linear wavefronts.
Sound, Wavefronts
Wavefronts join points in phase
Linear wavefronts
Wavefronts for compressional wave.
Rays – a ray is an arrow sketched through the wave fronts (perpendicular) to show direction of wave propagation.
Waves transfer energyEnergy is proportionalto the amplitude.
Less energy
More energy
For light increased amplitude increases brightness.
For sound: increased amplitude increases volume.
What does wave frequency (f) determine?
Wave type for EM waves.
Color for light.
Sound velocity solid
liquid
gas
In gas
hot faster.
cold slower.
Increasing velocity
The Doppler Effect
Stationary Source Emitting Waves all Directions. Circular wavefronts have = & f.
Doppler Effect from Moving Source
In front of source is less, behind is longer.
Another View
In front of source -short higher f:
hear higher pitch sound-see shorter light (blue).
behind source - longer lower f:
hear lower pitch soundsee longer light (red).
When objects are in relative motion:
a) Toward each other, f received increases.
b) Away from each other, f received decreases.
Doppler Effect
Resonance & Sympathetic Vibration
All objects have a naturalAll objects have a natural
frequency of vibration.frequency of vibration.
ResonanceResonance - the inducing- the inducingof vibrations of a naturalof vibrations of a naturalrate by a vibrating sourcerate by a vibrating source
having the same frequencyhaving the same frequency
““sympathetic vibrations”sympathetic vibrations”
Push at natural frequency, amplitude increases
Resonance:
An oscillatory system that is driven by a force with a frequency = to its natural frequency.
System will resonate – amplitude will increase.
Resonance & Sympathetic Vibration
Resonance occurs when a wave is in vicinity of an object & is vibrating at the natural frequency of the object. Object vibrates sympathetically at same frequency.
Continued vibration causes amplitude to increase.
mechanical universe resonance
A broad variety of tone colors exist because most sounds we perceive as pitch contain many frequencies.
• The predominant pitch The predominant pitch is called the is called the fundamental fundamental frequency. It is the frequency. It is the longest longest that forms a that forms a standing wave.standing wave.
Standing Wave patterns form notes.
Each string or pipe vibrates with particular frequencies of standing waves.
Other frequencies tend to die out.
Although we would perceive a string vibrating as a whole,
it vibrates in a pattern that appears erratic producing many different overtone pitches. What results are particular tone colors or timbres of instruments and voices.
Waveform with overtones.
Frequencies which occur along with the primary note are called the harmonic or overtone series.
When C is the fundamental the pitches below represent its first 15 overtones.
There are several standing waves which can be produced by vibrations on a string, or rope. Each pattern corresponds to vibrations which occur at a particular frequency and is known as a harmonic.
Harmonics
The lowest possible frequency at which a string could vibrate to form a standing wave pattern is known as the fundamental frequency or the first harmonic.
2nd Harmonic
Which One??
String Length L, & Harmonics
Standing waves can form on a string of length L, when the can = ½ L, or 2/2 L, or 3/2L etc.
Standing waves are the overtones or harmonics.
L = nn. n = 1, 2, 3, 4 harmonics. 2
Harmonic Frequencies
form where ½ can fit the string exactly.To calculate f:
L
nvf
2
f
vfv
2
nL
Substitute v/f for .
f
nvL
2
1st standing wave forms when = 2LFirst harmonic frequency is when n = 1 as below.
L
nvf
21
When n = 1 f is fundamental frequency or 1st harmonic.
L
nvf
22 For second harmonic n = 2.
f2 = v/L
Other standing waves with smaller wavelengths form other frequencies that ring out along with the fundamental.
In general,
The harmonic frequencies can be found where n = 1,2,3… and n corresponds to the harmonic. v is the velocity of the wave on the string. L is the string length.
L
nvfn 2
It is helpful to note that the distance between nodes on a standing wave is ½ .
½
Pipes and Air Columns
A resonant air column isA resonant air column issimply a standing simply a standing
longitudinallongitudinalwave system, much likewave system, much like
standing waves on a standing waves on a string.string. closed-pipe resonatorclosed-pipe resonator tube in which one end is tube in which one end is
openopenand the other end is closedand the other end is closed
open-pipe resonatoropen-pipe resonatortube in which both endstube in which both ends
are openare open
Open Pipe – open end has antinode.
Standing Waves in Open PipeBoth ends must be antinodes.
How much of the wavelength is the fundamental?
The 1st harmonic or fundamental can fit ½ into the tube.
Just like the string L = n 2
fn = nv2L
Where n, the harmonic is an integer.
Closed pipes must have a node at closed end and an antinode at the open end.
How many wavelengths??
Here is the next harmonic.How many ’s?
There are only odd harmonics possible.
L = 1/4.L = 3/4.L = 5/4
fn = nv where n = 1,3,5 … 4L
Beats – caused by constructive & destructive interference from 2
frequency sounds interacting.
• Beat Frequency heard is the difference between 2 frequencies.
• If a 50 Hz wave and a 60 Hz wave overlap, you hear beat of 10 Hz.
• hear beat frequencies
Traveling Waves Beats
Holt read 13 - 3
pg 509 38 - 39, 41, 44 46, 47 pg 499 #1 – 4
Start in class finish for hwk.