## Lecture

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## Lecture

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- Pages:
- 7
- School:
- University of California, San Diego
- Course:
- Phys 1c - Waves, Optics & Modern Physics

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Sound 14 49 Since the lengths and hence the wavelengths of the first harmonics of the strings are identical the ratio of their fundamental frequencies is f1 v 1 v v or f1 f1 v f1 v 1 v Thus the beat frequency heard when the two strings are sounded simultaneously is fbeat f1 f1 f1 1 v v From v F the speeds of transverse waves in the two strings are v 200 N and v 196 N so v v 196 N 0 980 200 N Therefore fbeat 523 H z 1 0 980 5 26 H z 507 506 CHAPTER 14 14 42 The distance between adjacent nodes is one quarter of the circumference dN N dA A 2 20 0 cm 5 00 cm 4 so 10 0 cm 0 100 m and f v 900 m s 9 00 103 H z 9 00 kH z 0 100 m The singer must match this frequency quite precisely for some interval of time to feed enough energy into the glass to crack it 14 45 Hearing would be best at the fundamental resonance so 4L 4 2 8 cm and 14 46 f v 340 m s 100 cm 3 3 0 10 H z 3 0 kH z 4 2 8 cm 1 m For a closed box the resonant frequencies will have nodes at both sides so the permitted n nv wavelengths will be L n 1 2 3 2 2f Thus fn nv With L 0 860 m and L 2 10 m the resonant frequencies are 2L fn n 206 H z for L 0 860 m for each n from 1 to 9 and fn n 84 5 H z for L 2 10 m for each n from 2 to 23 Sound 14 37 The facing speakers produce a standing wave in the space between them with the spacing between nodes being dN N 2 1 v 343 m s 0 214 m 2 f 2 800 H z If the speakers vibrate in phase the point halfway between them is an antinode of pressure at 1 25 m 0 625 m from either speaker 2 Then there is a node at 0 625 m 14 41 0 214 m 0 518 m 2 a node at 0 518 m 0 214 m 0 303 m a node at 0 303 m 0 214 m 0 0891 m a node at 0 518 m 0 214 m 0 732 m a node at 0 732 m 0 214 m 0 947 m and a node at 0 947 m 0 214 m 1 16 m from one speaker The speed of transverse waves in the string is v F 50 000 N 70 711 m s 1 000 0 10 2 kg m The fundamental wavelength is 1 2L 1 200 0 m and its frequency is f1 v 1 70 711 m s 58 926 H z 1 200

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