2. Waves and Sound Key Concepts: Pulses Wave Motion Types of WavesStanding Waves & Resonance Sound Doppler Effect

3. Pulses A single vibratory disturbance in a medium Transverse waves Velocity of the pulse v = √ T/(M/l) T = tension (N) ; M = mass (kg); l = length (m)

4. Principle of Superposition Incidence Reflection

5. Wave Motion Wave Train – series of waves Frequency = f (s -1 ) or Hertz (Hz) f = 1/T

6. λ= Wavelength (m) Crests = peaks of a wave Troughs = valleys of the wave A = amplitude, maximum displacement up or down (m)

7. Phase = the relative position of a point on a wave

8. Intensity (amplitude or volume) Pitch (frequency)

9. Types of Waves Mechanical waves

10. Electromagnetic waves

11. Longitudinal or compression waves The vibrations create pressure differences that expand and contract Vibrations must be perpendicular to the direction of apparent motion

12. Polarization

13. Standing Waves & Resonsance Fundamental mode Standing wave Nodal points λ = 2l λ = l λ = 2/3l λ = 1/2l

14. Resonance The build up of wave energy due to constructive interference

15. SOUND Acoustics acoustical waves SubstanceVelocity Gases (0°) carbon dioxide Air Helium 259 331 965 Liquids (25°) Ethyl alcohol Water, pure Water, sea 1207 1498 1531 Solids Lead Wood Iron & steel Aluminum Glass (pyrex) 1200 -4300 -5000 5100 5170

16. Ultrasonic (>20,000 Hz) Loudness = amplitude Pitch = frequency Beats = regions of constructive & destructive interference Human hearing can detect sound from 20- 20,000HZ

17. Interference dependent on the path-length difference For 2 point sources of sound, A and B: l A - l B = to a whole multiple of the wavelength, nλ Destructive interference will occur if the path-length = an odd multiple of the half- wavelengths (n+1/2) λ

18. Diffraction When a wave encounters a boundary, it appears to bend around the corners of the boundary

19. Intensity of sound Measured in decibels (dB) A logarithmic (base 10) system l = the intensity in units of watts per square meter L 0 =the barely audible intensity 10 -12 watt per square meter

20. Common decibel measurements SoundIntensity (dB) Whisper Conversation Loud sound Deafening sound Painful sound Damaging sound 30 60 70-90 100 120 140

21. Doppler effect As a sound approaches the pitch increases, as it passes the pitch is decreased The relationships are given by and v= wave velocity v s = relative velocity of source

23. If the source velocity equals the wave velocity, a strong interference pattern builds up in front of the source The regions of constructive interference are called shock waves The ration of the source velocity to the wave velocity is called the MACH NUMBER

24. Air Columns v = λ f = (4L) f 1 v= λ f = (4/3L) f 3  f 3 = ¾ v/L = 3 f 1 v= λ f = (4/2L) f 2  f 2 = ½ v/L = 2 f 1

25. Beats – when 2 waves of the same frequency pass through each other f beat = |f b - f b |