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# Standing Waves

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### Standing Waves

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