The Nature of Waves. Wave: Any disturbance that transmits energy through matter or empty space.
WAVES AND SOUND 5% AP Physics B. 13.7 Waves – what is a wave? Wave – a vibration or disturbance...
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Transcript of WAVES AND SOUND 5% AP Physics B. 13.7 Waves – what is a wave? Wave – a vibration or disturbance...
WAVES AND SOUND 5%AP Physics B
13.7 Waves – what is a wave?Wave – a vibration or disturbance in space
Mechanical Wave requirements:1. Source of disturbance2. Medium to travel through
13.7 Waves - types of wavesLongitudinal
Longitudinal Wave – medium moves parallel with the wave motion
2 parts:Compression- an area of high molecular density and pressure (crests)Rarefaction - an area of low molecular density and pressure (troughs)
13.7 Waves - types of waves
Transverse Wave - medium moves perpendicular with the wave motion
Transverse
Wave parts – crest, trough, wavelength, amplitude, frequency, periodhttp://physics.bu.edu/~duffy/semester1/c20_trans_long.html
• Frequency – of waves passing a specified point per second• Symbol: f Units: Hertz, Hz; 1 Hz = 1/s
• Period – time it takes 1 wave to pass a specified point• Symbol: T Units: s• T = 1/f http://physics.bu.edu/~duffy/semester1/c20_wave_fvl.html
• Wavelength – horizontal distance between successive waves• Symbol: λ Units: m
• Amplitude – max vertical distance medium moves from equilibrium• Symbol: A Units: m
• Wave speed – rate at which wave moves horizontally• v = fλ http://physics.bu.edu/~duffy/semester1/c20_wave_speed.html
13.8 Frequency, Amplitude, & Wavelength
13.8 Frequency, Amplitude, & Wavelength – Example A harmonic wave is traveling along a rope. It is observed that the
oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength?
33.1
425.0
/425.010
425.0
33.130
40
sec
fv
smt
xv
Hzcycles
f
wave 0.0319 m/s
13.9 The Speed of Waves on Strings• Transverse wave on a stretched spring
• Two things to consider:• Vertical vibration speed• Wave speed (horizontal)
• v =•F – tension in the string•µ - linear density, mass of string per unit length• µ = mass/length
13.10 Interference of Waves• “Two traveling waves can meet and pass through each other
without being destroyed or altered”• Superposition principal – two waves moving through the
same medium pass, resulting wave is found by adding the two waves point by point
Constructive interference Destructive
interference
13.11 Reflection of Waves• Wave pulse bounces off a rigid
boundary reflected wave is inverted
http://physics.bu.edu/~duffy/semester1/c21_int_reflections.html
• Wave pulse bounces off movable boundary reflected wave is not inverted
14.1 Producing a Sound Wave• Longitudinal waves• Requires a medium through which to travel• http://physics.bu.edu/~duffy/semester1/c20_disp_pressure.html • Article: http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroSound.xml
Compression Rarefaction
14.3 The Speed of Sound• Speed of sound in a gas: v =
• B = bulk modulus• Ρ = equilibrium density
• Speed of sound in air: vair = (331 m/s)
• See p.476 for table of speeds of sound in various mediums
14.5 Spherical & Plane Waves
• Intensity of a sound wave:• I = average power/area = Pav/A = Pav/4πr2
A spherical wave propagating radially outward from an oscillating sphere. Key idea: The intensity of the wave varies as 1/r2.http://physics.bu.edu/~duffy/semester1/c20_sound_intensity.html
• Frequency of sound (and light) shifts if the source is moving towards you or away from you
•
• Towards higher frequency• Away lower frequencyhttp://physics.bu.edu/~duffy/semester1/c21_doppler.html
Article: http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html
14.6 Doppler Effect
+vo when observer moving towards source-vo when observer moving away from source+vs source moving away from observer-vs source moving towards observer
Think about it:If the source and observer are moving towards each other, the waves get bunched together and the frequency goes up.If the source and observer are moving further apart, the frequency will decrease as the waves get stretched apart.Keep this in mind as you apply the equation!
14.7 Interference of Sound Waves
• Constructive interference occurs when the path difference between two waves’ motion is zero or some integer multiple of wavelengths• Path difference = nλ (n = 0, 1, 2, … )
• Destructive interference occurs when the path difference between two waves’ motion is an odd half wavelength• Path difference = (n + ½)λ (n = 0, 1, 2, … )
14.8 Standing WavesA standing wave is produced when a wave that is traveling
is reflected back upon itself. There are two main parts to a standing wave:
• Antinodes – Areas of MAXIMUM AMPLITUDE• Nodes – Areas of ZERO AMPLITUDE.• Ends of string are nodes (b/c fixed)
Distance between antinodes or nodes = ½wavelength
http://physics.bu.edu/~duffy/semester1/c21_int_standing.html
Beats:
http://physics.bu.edu/~duffy/semester1/c22_beats.html
14.8 Standing Waves• Harmonic Series Frequencies: (Equation derived using f=v/λ and vwaveonstring= )
Link to video clips of waves vibrating at harmonic frequencies: http://www.acoustics.salford.ac.uk/feschools/waves/string.htm
14.9 Forced Vibrations & ResonanceSound Waves are a common type of standing wave as they are
caused by RESONANCE. Resonance – when a FORCED vibration matches an object’s
natural frequency thus producing vibration, sound, or even damage.
One example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible. (play video clip of singing shattering glass)
In 1940, turbulent winds set up torsional vibrations in the Tacoma Narrows Bridge, causing it to oscillate at a frequency near one of the natural frequencies of the bridge structure. (b) Once established, this resonance condition led to the bridge’s collapse. A number of scientists, however, have challenged the resonance interpretation.
14.10 Standing Waves in Air Columns - Instruments
The production of sound involves setting up a wave in air. To set up a CONTINUOUS sound you will need to set a standing wave pattern.
Three LARGE CLASSES of instruments• Stringed - standing wave is set up in a tightly stretched string
• Standing wave on a string• Percussion - standing wave is produced by the vibration of
solid objects• Standing wave through medium
• Wind - standing wave is set up in a column of air that is either OPEN or CLOSED• Standing wave in air column
14.10 Standing Waves in Air Columns - Open Pipe Harmonics
OPEN PIPES- antinode on BOTH ends of the tubeWhat is the SMALLEST length of pipe you can have to
hear a sound?
You will get your FIRST sound when the length of the pipe equals one-half of a wavelength.
14.10 Standing Waves in Air Columns - Open Pipe Harmonics
Since harmonics are MULTIPLES of the fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH.
The picture above is the SECOND harmonic or the FIRST OVERTONE.
14.10 Standing Waves in Air Columns - Open Pipe Harmonics
Another half of a wavelength would ALSO produce an antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends
The picture above is the THIRD harmonic or the SECOND OVERTONE.
CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!
14.10 Standing Waves in Air Columns - Open Pipe Harmonics
CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!
In Open Pipes: ends are always antinodes
Harmonics are MULTIPLES of the fundamental frequency:
𝒇 𝒏=𝒏𝒗𝟐𝑳
=𝒏 𝒇 𝟏𝐧=𝟏 ,𝟐 ,𝟑 ,…
14.10 Standing Waves in Air Columns - Closed Pipe Harmonics
Closed Pipes - antinode at one end and a node at the other.
Each sound you hear will occur when an antinode appears at the top of the pipe.
What is the SMALLEST length of pipe you can have to hear a sound?
You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength.
This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.
14.10 Standing Waves in Air Columns - Closed Pipe Harmonics
In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NOSOUND is produced
14.10 Standing Waves in Air Columns - Closed Pipe Harmonics
In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced.
CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!
14.10 Standing Waves in Air Columns - Closed Pipe Harmonics
• CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!
In Closed Pipes: one end is always node, one end is always antinode
Harmonics are ODD MULTIPLES of the fundamental frequency:𝒇 𝒏=𝒏
𝒗𝟒 𝑳
=𝒏 𝒇 𝟏𝒏=𝟏 ,𝟑 ,𝟓 ,…
Helpful Links:• http://www.phys.unsw.edu.au/jw/strings.html#modes • http://
www.acoustics.salford.ac.uk/feschools/waves/string.htm