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Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
Standing  Waves
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Standing Waves

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Transcript

  • 1. Standing Waves A guide to what they are and where they are used
  • 2. To summarise so far:
        • Waves superpose when they meet
        • They can interfere constructively when ‘In-Phase’ and destructively when ‘anti-phase’
        • Waves interfere in a stable manner when they are coherent – they have a constant phase difference
        • Waves can be represented by a phasor that rotates anticlockwise
        • The angular movement can be represented in Radians, where 2π Radians is the equivalent to 360 o and 1 wavelength (λ)
  • 3. This lesson we will
    • See how a standing wave in a string is set up
    • Understand how a standing wave is formed in terms of wavelengths
    • Find out what a fundamental frequency of a standing wave is
    • Understand the term resonance, harmonic, node and antinode
  • 4. Standing Waves
    • These are caused by 2 waves interfering
    • They are usually caused by a wave and its reflection
  • 5. Let’s see one in action...
  • 6. Standing Wave Properties
    • A string has a wavelength that is double the length of string
    1/2 Wavelength
  • 7. Standing Wave Properties
    • What is the next wavelength?
    • Try to draw it...
    1/2  Length = n  /2 I.e. it is a multiple of half wavelengths Length
  • 8. Wavelengths
    • For all values of n, wavelengths are multiples of 1/2 
    • What is the equation for speed?
    • What are the wavelengths opposite if L = 30cm?
  • 9. Fundamental Frequency
    • This is the lowest frequency that a system can resonate at - it is the lowest frequency that a standing wave can form at on a string
    • Using; Speed = Frequency x Wavelength
    • Therefore
    • Fundamental Frequency = speed / 2L
    • What is the fundamental frequency the previous string (30cm) assuming the speed is 60ms -1 ?
  • 10. Fundamental Frequency
    • What is the fundamental frequency for the previous string (30cm) assuming the speed is 60ms -1 ?
    1/2  30cm Fundamental Frequency = 60 / 2 x 0.3 = 100Hz
  • 11. Standing Wave Properties
    • Harmonics
      • These are the multiples of the fundamental frequency
      • For string this is a whole number
      • Frequency = v/  L
      • harmonics =
        • n x frequency
  • 12. Harmonics
    • An harmonic is a multiple of the fundamental frequency
    • For our piece of string, what are the harmonics?
    1/2  30cm Harmonics = n x Fundamental Frequency = 200, 300, 400…. N x 100Hz
  • 13. Nodes and Antinodes
    • These are areas of the wave that;
      • Node - always add up to zero
      • Antinode - waves combine to make a large oscillation
  • 14. Some Questions
    • 1.A source of sound waves of frequency 570Hz emits a note of wavelength 0.6m in air at 20 o C. What is the speed of sound at this temperature?
    • 2.A stationary wave is formed in a string with antinodes every 150mm. What is the wavelength of the standing wave?
    • 3.A loudspeaker points directly at a wall 3m away and emits a note of frequency 680Hz. A standing wave is formed. If the speed is 340m/s what will be the separation between minimum intensities (nodes)?
  • 15. Some Questions
    • 1.A source of sound waves of frequency 570Hz emits a note of wavelength 0.6m in air at 20 o C. What is the speed of sound at this temperature? 342m/s
    • 2.A stationary wave is formed in a string with antinodes every 150mm. What is the wavelength of the standing wave? 300mm
    • 3.A loudspeaker points directly at a wall 3m away and emits a note of frequency 680Hz. A standing wave is formed. If the speed is 340m/s what will be the separation between minimum intensities (nodes)? 0.25m

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