Physics214Week13

Physics214Week13 - This Week Waves Standing waves Musical...

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This Week Waves Standing waves Musical instruments, guitars, pianos, organs Interference of two waves tuning a piano, color of oil films Polarisation Why have polaroid sun glasses? Electromagnetic waves and telescopes How do we see color 12/09/11 Physics 214 Fall 2011 1

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12/09/11 Physics 214 Fall 2011 2 Periodic waves One can propagate waves which are a single complicated pulse e.g. an explosion or a complicated continuous wave e.g. the wind. We will focus on regular repetitive waves These waves have a pattern which repeats and the length of one pattern is called the wavelength λ The number of patterns which pass a point/second is called the frequency f and if the time for one pattern to pass is T then f = 1/T v = λ/T = fλ λ
12/09/11 Physics 214 Fall 2011 3 Waves on a string If we shake the end of a rope we can send a wave along the rope. The rope must be under tension in order for the wave to propagate v = √(F/μ) F = TENSION μ = MASS/UNIT LENGTH

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12/09/11 Physics 214 Fall 2011 4 Standing waves If two identical waves exist on the same string but traveling in opposite directions the result can be standing waves in which some points never have a deflection, these are called nodes Some points oscillate between plus and minus the maximum amplitude, these are called antinodes. Standing waves provide the notes on musical instruments. When a string is secured at both ends and plucked or hit the generated waves will travel along the string and be reflected and set up standing waves.
12/09/11 Physics 214 Fall 2011 5 Musical notes Each end of the string must be a node so the possible standing waves must be multiples of λ/2 Fundamental f = v/λ = v/2L 2 nd Harmonic f = v/λ = v/L 3 rd Harmonic f = v/λ = 3v/2L Musical sound is a mixture of harmonics modified by the body of the instrument. v = √(F/μ) so a piano or a violin is tuned by changing the tension in the string

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12/09/11 Physics 214 Fall 2011 6 Closed organ pipe Node at one end and an antinode at the other Fundamental f = v/4L 2 nd Harmonic f = 3v/4L 3 rd Harmonic f = 5v/4L The velocity of sound in air is v = 340m/s
12/09/11 Physics 214 Fall 2011 7 Beats If two waves have slightly different frequencies then the sum has a frequency which is f 1 – f 2. The human ear can detect beats and this is used to tune an instrument. For example using a tuning fork at a known frequency and adjusting a piano string until no beats heard f = f 1 – f 2

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12/09/11 Physics 214 Fall 2011 8 Doppler effect The Doppler effect is the change in frequency of a wave when the source and observer are moving. As the source is approaching the frequency increases and if it is receding the frequency decreases h t t p http://www.physics.purdue.edu/class/applets/phe/dopplereff.htm
12/09/11 Physics 214 Fall 2011 9 Sonic boom Sonic boom At each point on the path the sound wave expands radially and they all combine along a single wave front which is a pressure wave causing us to hear the boom http://www.phy.ntnu.edu.tw/java/airplane/airplane.html

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Physics214Week13 - This Week Waves Standing waves Musical...

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