PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 23 Last Lecture Sound Speed of sound in fluid for solid replace Intensity B Y P I A Intensity Level dB v B Spherical Waves 10 log10 I I 0 10 10 P I 2 4 r I Io I0 10 12 W m2 Doppler Effect Moving Observer Towards source v vo v Away from source Fig 14 8 p 435 Slide 12 v vo v Fig 14 9 p 436 Slide 13 v speed of sound vO speed of observer Doppler Effect Source in Motion vs T vs v 1 vs v f v v f f v vs Doppler Effect Source in Motion Approaching source v f f v vs Source leaving v f f v vs Example 14 6 An train has a brass band playing a song on a flatcar As the train approaches the station at 21 4 m s a person on the platform hears a trumpet play a note at 3520 Hz DATA vsound 343 m s a What is the true frequency of the trumpet a 3300 Hz b What is the wavelength of the sound b 9 74 cm c If the trumpet plays the same note after passing the platform what frequency would the person on the platform hear c 3106 Hz Shock Waves Sonic Booms When the source velocity exceeds the speed of sound Fig 14 11 p 439 Slide 15 Application speed radar Application weather radar Both humidity reflected intensity and speed of clouds doppler effect are measured Doppler Effect Both Observer and Source Moving v vo v v s Switch appropriate signs if observer or source moves away Example 14 7 At rest a car s horn sounds the note A 440 Hz The horn is sounded while the car moves down the street A bicyclist moving in the same direction at 10 m s hears a frequency of 415 Hz DATA vsound 343 m s What is the speed of the car Assume the cyclist is behind the car 31 3 m s Example 14 8a A train has a whistle with a frequency of a 1000 Hz as measured when both the train and observer are stationary For a train moving in the positive x direction which observer hears the highest frequency when the train is at position x 0 Observer Observer Observer Observer A B C D has has has has velocity velocity velocity velocity VA 0 and has position XA 0 VB 0 and has position XB 0 VC 0 and has position XC 0 VD 0 and has position XD 0 Example 14 8b A train has a whistle with a frequency of a 1000 Hz as measured when both the train and observer are stationary A train is moving in the positive x direction When the train is at position x 0 An observer with V 0 and position X 0 hears a frequency a 1000 Hz b 1000 Hz c Can not be determined Example 14 8c A train has a whistle with a frequency of a 1000 Hz as measured when both the train and observer are stationary A train is moving in the positive x direction When the train is at position x 0 An observer with V 0 and position X 0 hears a frequency a 1000 Hz b 1000 Hz c Can not be determined Example 14 8d A train has a whistle with a frequency of a 1000 Hz as measured when both the train and observer are stationary A train is moving in the positive x direction When the train is at position x 0 An observer with V 0 and position X 0 hears a frequency a 1000 Hz b 1000 Hz c Can not be determined Standing Waves Consider a wave and its reflection yright yleft yright yleft x Asin 2 ft x x 0 3 A 1sin 2 cos 2 ft cos 2 sin 2 ft 4 2 5 x Asin 2 ft x x 0 3 A 1sin 2 cos 2 ft cos 2 sin 2 ft 4 2 5 x 2Asin 2 cos 2 ft Standing Waves yright yleft x 2Asin 2 cos 2 ft Factorizes into x piece and t piece Always ZERO at x 0 or x m 2 Resonances Integral number of half wavelengths in length L n L 2 Fig 14 16 p 442 Slide 18 Nodes and anti nodes A node is a minimum in the pattern An antinode is a maximum Fundamental 2nd 3rd Harmonics 2nd harmonic n L 2 3rd harmonic Fundamental n 1 Fig 14 18 p 443 Slide 25 Example 14 9 A cello string vibrates in its fundamental mode with a frequency of 220 vibrations s The vibrating segment is 70 0 cm long and has a mass of 1 20 g a Find the tension in the string a 163 N b Determine the frequency of the string when it vibrates in three segments b 660 Hz Beats Interference from two waves with slightly different frequency Beat Frequency Derivation After time Tbeat two sounds will differ by one complete cycle f1Tbeat n1 n 2 1 f2Tbeat 1 Tbeat fbeat 1 f1 f2 1 Tbeat fbeat f1 f2 Beats Demo Standing waves in Pipes Open both ends n n 2 Same expression for closed at both ends Standing waves in Pipes Closed one end n 2n 1 4 Example 14 10 An organ pipe of length 1 5 m is open at one end What are the lowest two harmonic frequencies DATA Speed of sound 343 m s 57 2 Hz 171 5 Hz Example 14 11 An organ pipe open at one end and closed at the other is designed to have a fundamental frequency of 440 Hz Assuming the speed of sound is 343 m s a What is the length of the pipe a 19 5 cm b What is the frequency of the next harmonic b 1320 Hz Interference of Sound Waves Assume sources a and b are coherent If observer is located ra and rb from the two sources Source a Source b rb ra ra rb n for maximum ra rb n 1 2 for minimum Observer Example 14 12 A pair of speakers separated by 1 75 m are driven by the same oscillator at a frequency of 686 Hz An observer starts at one of the speakers and walks on a path that is perpendicular to the separation of the two speakers Assume vsound 343 m s a What is the position of the last intensity maximum a 2 81 m b What is the position of the last intensity minimum b 6 00 m c What is the position of the first intensity maximum c 27 cm
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