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Standing Waves

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• 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