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THE PHYSICS OF MUSIC ♫ MUSIC • Musical TonePleasing sounds that have periodic wave patterns. • Quality of sounddistinguishes identical notes from different instruments. http://www.animations.physics.unsw.edu. au/jw/sound-pitch-loudness-timbre.htm Beats- the change in sound intensity due to the interference of sound. Beat Frequencythe number of maximum intensity points per second. 2 beats Beat Frequency BF = # Beats seconds or BF = | f1 – f2 | * Two possible answers Ex. A sound with a frequency of 400Hz interferes with a second sound. If this produces 20 beats in 5.0 seconds, what is the frequency of the second sound? BF= 20beats/ 5 sec = 4 beats/sec 4 beats/sec = | 400Hz - f2 | 396Hz or 404 Hz STANDING WAVES Two identical waves traveling in opposite directions. N –node A- antinode MODES OF VIBRATION Fundamental mode, lowest pitch. λ = 2L First overtone, second harmonic, λ=L Second overtone, 3 rd harmonic, λ = 2/3L Third overtone, 4th harmonic, λ = 1/2L HARMONICS Whole number multiples of the fundamental frequency. Doubling the frequency will raise the pitch one octave (8 notes) String Instruments LAWS OF STRINGS Law of Length: As the length of a string increases, frequency and pitch decreases. Law of Diameter: As the diameter of a string increases, frequency decreases. Law of Tension: As the tension on a string increases, frequency and pitch increases. Law of Density: If a more dense string is used, the frequency and pitch decreases. Woodwind and Brass Use resonating air columns to make music. RESONANCE IN AIR COLUMNS Resonance occurs every half wavelength. λ = 2L f1 = v/2L L Wavelength depends of the length and diameter of the resonating pipe. λ = 2( L + 0.8d) L- length (m) d- diameter (m) Ex: An open plastic pipe will resonate at its lowest frequency when a tuning fork is held over it. If the pipe has a length of 60cm and a diameter of 4.0cm what is the wavelength? λ = 2( L + 0.8d) λ = 2(0.6m + 0.8(0.04m) λ = 1.264m Just for fun! The Rubens Tube • http://www.youtube.com/watch?v=M021bsxM_k • http://www.youtube.com/watch?v=gpCquU WqaYw