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