1. WAVES AND SOUND 5% AP Physics B

2. 13.7 Waves – what is a wave? Wave – a vibration or disturbance in space Mechanical Wave requirements: 1.Source of disturbance 2.Medium to travel through

3. 13.7 Waves - types of waves Longitudinal 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)

4. 13.7 Waves - types of waves Transverse Wave - medium moves perpendicular with the wave motion Transverse Wave parts – crest, trough, wavelength, amplitude, frequency, period http://physics.bu.edu/~duffy/semester1/c20_trans_long.html

5. Frequency – of waves passing a specified point per second Symbol: fUnits: Hertz, Hz; 1 Hz = 1/s Period – time it takes 1 wave to pass a specified point Symbol: TUnits: s T = 1/f http://physics.bu.edu/~duffy/semester1/c20_wave_fvl.html http://physics.bu.edu/~duffy/semester1/c20_wave_fvl.html Wavelength – horizontal distance between successive waves Symbol: λUnits: m Amplitude – max vertical distance medium moves from equilibrium Symbol: AUnits: m Wave speed – rate at which wave moves horizontally v = fλ http://physics.bu.edu/~duffy/semester1/c20_wave_speed.html http://physics.bu.edu/~duffy/semester1/c20_wave_speed.html 13.8 Frequency, Amplitude, & Wavelength

6. 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? 0.0319 m/s

7. 13.9 The Speed of Waves on Strings

8. 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

9. 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

10. 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.xmlhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroSound.xml Compression Rarefaction

11. 14.3 The Speed of Sound

12. 14.5 Spherical & Plane Waves Intensity of a sound wave: I = average power/area = P av /A = P av /4πr 2 A spherical wave propagating radially outward from an oscillating sphere. Key idea: The intensity of the wave varies as 1/r 2. http://physics.bu.edu/~duffy/semester1/c20_sound_intensity.html

13. 14.6 Doppler Effect +v o when observer moving towards source -v o when observer moving away from source +v s source moving away from observer -v s 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. 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, … )

15. 14.8 Standing Waves A 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

16. 14.8 Standing Waves Link to video clips of waves vibrating at harmonic frequencies: http://www.acousti cs.salford.ac.uk/fe schools/waves/stri ng.htm http://www.acousti cs.salford.ac.uk/fe schools/waves/stri ng.htm

17. 14.9 Forced Vibrations & Resonance Sound 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.

18. 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

19. 14.10 Standing Waves in Air Columns - Open Pipe Harmonics OPEN PIPES- antinode on BOTH ends of the tube What 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.

20. 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.

21. 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!

22. 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:

23. 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.

24. 14.10 Standing Waves in Air Columns - Closed Pipe Harmonics In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced

25. 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!

26. 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:

27. Helpful Links: http://www.phys.unsw.edu.au/jw/strings.html#modes http://www.acoustics.salford.ac.uk/feschools/waves/strin g.htm http://www.acoustics.salford.ac.uk/feschools/waves/strin g.htm