Welcome to PHYS 1240 Sound and Music Professor John Price. Cell Phones off Laptops closed Clickers on Transporter energized
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1 Welcome to PHYS 1240 Sound and Music Professor John Price Cell Phones off Laptops closed Clickers on Transporter energized Guitar Tuning bar pair Big string Gong rod
2 Beats: Two Sources with Slightly Different Frequency Russell: Superposition of Waves (scroll down) Figure from Physclips PhET Fourier Applet Beat Frequency = Difference of Frequencies
3 7-1 E4 = Hz Eb4 = Hz What is the beat frequency if I play both notes at the same time? a) Hz b) 29.6 Hz c) 10.0 Hz d) 4.3 Hz e) None of the above Can we hear the beating? Tuning Fork demo, Guitar demo
4 Review Units and SI prefix system: N = μn x(t) = A sin(360 t/t + ϕ) f = 1 2π s m Normal or natural modes Air pressure, pressure = force/area Speed of sound νν = λλ TT = λλλλ
5 Standing Waves on Strings Running vs. Standing Waves UNSW: Guitars: Strings: Standing waves Standing Wave = Superposition of two running waves The standing wave has the same wavelength and frequency as the running waves it is made from.
6 Sinusoidal running wave v Position (m) Wavelength Wavelength λ (m) vv = λλ TT = λλ ff Frequency Period Same formula for standing wave!
7 7-2 Which of the two points on the string oscillates with the higher frequency? A) Left point B) Right point C) They both have the same frequency
8 7-3 Below is a picture of a standing wave on a 30 meter long string. What is the wavelength of running waves that the standing wave is made from? A.30 m B.60 m L = 30 m C.15 m D.Impossible to tell
9 7-4 Below is a picture of a standing wave on a 30 meter long string. What is the wavelength of the running waves that the standing wave is made from? A.30 m B.60 m 30 m C.10 m D.20 m E.Impossible to tell
10 A string is clamped at both ends and then plucked so that it vibrates in a standing wave between two extreme positions a and c. (Let upward motion correspond to positive velocities.) When the string is in position b, the instantaneous velocity at different locations along the string A: is zero everywhere. B: is positive everywhere. C: is negative everywhere D: depends on position.
11 7-6 A string is clamped at both ends and then plucked so that it vibrates in a standing wave between two extreme positions a and c. (Let upward motion correspond to positive velocities.) When the string is in position c, the instantaneous velocity at different locations along the string... A: is zero everywhere. B: is positive everywhere. C: is negative everywhere D: depends on position.
12 7-7 Could you observe standing waves made from running waves with a wavelength of 2/3 m on a string of length 1 m? If so, what mode would that be? A.Yes, n = 1 B.Yes, n = 2 C.Yes, n = 3 D.Yes, n = 4 E. No
13 String Mode Frequencies from ff = vv tt λλ LL λλ 1 = 2LL 1 ff 1 = 1 vv tt 2LL λλ 2 = 2LL 2 ff 2 = 2 vv tt 2LL λλ 1 = 2LL 3 ff 3 = 3 vv tt 2LL ff nn = nn vv tt 2LL nn = 1, 2, 3, 4,
14 ff nn = nn vv tt 2LL nn = 1, 2, 3, 4, What does it mean?
15 ff nn = nn vv tt 2LL nn = 1, 2, 3, 4, What does it mean? ff 1 = 1 vv tt 2LL ff 2 = 2 vv tt 2LL ff 3 = 3 vv tt 2LL ff 4 = 4 vv tt 2LL and so on.
16 ff nn = nn ff 1 nn = 1, 2, 3, 4, This is a Harmonic Series demo string versus bar good strings and bad strings
17 Are string modes normal modes? LL λλ 1 = 2LL 1 ff 1 = 1 vv tt 2LL λλ 2 = 2LL 2 ff 2 = 2 vv tt 2LL λλ 1 = 2LL 3 ff 3 = 3 vv tt 2LL ff nn = nn vv tt 2LL nn = 1, 2, 3, 4,
18 Normal Modes 1. The number of degrees of freedom is the number of numbers needed to specify the positions of the moving parts. infinite 2. The number of normal modes is equal to the number of degrees of freedom. infinite 3. In a normal mode motion, all points move sinusoidally with the same frequency and all points move through equilibrium at the same time. 4. In general, the frequencies of different modes will be different. 5. In real systems, normal modes are always damped. 6. A general motion is a superposition (sum) of normal mode motions. Yes! String modes are normal modes with frequencies that form a harmonic series
19 A (normal) mode is a motion where every point moves with the same frequency LL A node is a place where a mode has no motion An anti-node is a place where a mode has maximum motion
20 7-8 A string vibrates with a fundamental frequency of 220 Hz. Besides 220 Hz, which of the following are resonant frequencies you might also observe? i) 110 Hz ii) 330 Hz iii) 440 Hz A: i only B: ii only C: iii only D: i and ii E: all three
21 Welcome to PHYS 1240 Sound and Music Professor John Price Cell Phones off Laptops closed Clickers on Transporter energized Guitar, Bansuri Homelab string Demo sounding the harmonics Clavichord YouTube Archlute YouTube Oud YouTube Bansuri YouTube Review slide 13 Demo homelab 2 Oud and the rose
22 A string on an instrument plays an A (440 Hz) when plucked. If you lightly touch the string ½ way from one end, and then pluck, you are mostly likely to hear 8-1 A: Still 440 Hz B: 220 Hz C: 880 Hz D: Something entirely different
23 A string has a fundamental frequency f The second harmonic has frequency f 2 = 2f 1, or one octave higher. Which harmonic is TWO octaves above f 1? A) f 3 B) f 4 C) f 5 D) f 8 E)??
24 8-3 How many interior nodes are there in a standing wave with n = 10? A. 9 B. 10 C. 11 D. I would have to draw it and count n=1 n=2 n=3
25 8-4 A string vibrates in the fundamental, producing an A (440 Hz) sound. Suppose the speed of sound in the air could be suddenly doubled (but the string is left unchanged) What would you HEAR? A) Same pitch (440 Hz) B) Lower pitch C) Higher pitch, but not double D) Double pitch = one octave higher E)??
26 8-5 A string on an instrument plays an A (440 Hz) when plucked. If you put your finger down hard (pushing the string to the fret or fingerboard), one third of the way along the string, and then pluck the longer side, you are mostly likely to hear A: 3*440Hz B: (1/3)*440 Hz C: 3/2 * 440 Hz D: 2/3 * 440 Hz E: Something different Clavichord YouTube
27 Velocity of Transverse Waves on a String tension (N) v t = F µ mass/length (kg/m) Book uses v s But it is not the speed of sound in air!
28 Why is this the right formula? 1 F 1 F / L s f 1 = 2L µ = 2 µ L m
29 8-6 v t = F µ What are the units of F? A. m/s B. kg C. N D. kg/m E. m/s 2
30 8-7 v t = F µ What are the units of μ? A. m/s B. kg C. N D. kg/m E. m/s 2
31 8-8 v t = F µ What are the units of v t? A. m/s B. kg C. N D. kg/m E. m/s 2
32 8-9 v t = F µ If the tension is increased by a factor of 9 what happens to the speed of waves on a string? A. Goes up by a factor of 3 B. Goes up by a factor of 4.5 C. Goes up by a factor of 9 D. Goes up by a factor of 81 E. None of these / I don t know What happens to the frequency of the fundamental?
33 8-10 If you want to lower the pitch of a string by an octave, what must be done to its tension? A. Raise it by a factor of 4 B. Lower it by a factor of 4 C. Lower it by a factor of 2 D. Lower it by a factor of 6 E. None of these / I don t know
34 8-11 If you increase tension by a factor of 4 A) The frequency of the fundamental doubles, all other harmonics stay the same as they were B) The frequency of every harmonic doubles C) None of the frequencies change, the wavelengths double D) f 1 goes up by 2, f 2 by 4, (etc ) E) Something else?
35 8-12 The high E string (1 st string) of a guitar is two octaves above the low E string (6 th string). They both have about the same tension and length. The mass per unit length μ of the 6 th string is how many times greater than the mass per unit length of the 1 st string? A. 2 B. 4 C. 6 D. 8 E. 16 Archlute on YouTube Overwound strings invented about 1650
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