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Chapter 15: Waves and Sound

motion of “pulse”. actual motion of string. Chapter 15: Waves and Sound. Example: pulse on a string speed of pulse = wave speed = v depends upon tension T and inertia (mass per length  ). Reflections at a boundary fixed end = “hard” boundary Pulse is inverted.

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Chapter 15: Waves and Sound

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  1. motion of “pulse” actual motion of string Chapter 15: Waves and Sound • Example: pulse on a string • speed of pulse = wave speed = v • depends upon tension T and inertia (mass per length )

  2. Reflections at a boundary • fixed end = “hard” boundary • Pulse is inverted • Reflections at a boundary • free end = “soft” boundary • Pulse is notinverted

  3. Reflections at an interface • light string to heavy string = “hard” boundary • faster medium to slower medium • heavy string to light string = “soft” boundary • slower medium to faster medium • Principle of Superposition: When Waves Collide! • When pulses pass the same point, • add the two displacements

  4. A • Periodic Waves • a.k.a. Harmonic Waves, Sine Waves ... • Important characteristics of periodic waves • wave speedv: the speed of the wave, which depends upon the medium only. • wavelength: : (greek lambda) the distance over which the wave repeats, it is also the distance between crests or troughs. • frequencyf : the number of waves which pass a given point per second. The period of the wave is related to the frequency by T = 1/f. • Wavelength, speed and frequency are related by: • v =  f • Amplitude A: the maximum displacement from equilibrium. The amplitude does not affect the wave speed, frequency, wavelength, etc. •  Elastic Potential Energy and Kinetic Energy associated with wave depend upon Amplitude. • Energy per time (power) carried by a wave is proportional to the square of the amplitude. • “Loudness” depends upon amplitude.

  5. Types of waves • Transverse Waves: “disturbance” is perpendicular to wave velocity, such as for waves on a string. (disturbance is a shear stress, only occurs in solids!) • Longitudinal Waves: “disturbance” is parallel to wave velocity, such as the compression waves on the slinky. • Water surface waves: mixture of longitudinal and transverse

  6. Standing Waves • vibrations in fixed patterns • effectively produced by the superposition of two traveling waves • y = y0sin(x/lt/T) • constructive interference: waves add • destructive interference: waves cancel  = 2L  = 2L  = 2L  = 2L node antinode antinode

  7.  = 2L  = 2L  = 2L  = 2L • Resonance • When a system is subjected to a periodic force with a frequency equal to one of its natural frequencies, energy is rapidly transferred to the system. • examples: • musical instruments with fundamental or overtones • mechanical vibrations

  8. Example: What is the wave speed of a guitar string whose fundamental frequency is 330 Hz if the length of string free to vibrate is 0.651m? What is the tension in the string of the string’s linear mass density is 0.441 g/m3?

  9. Sound Waves: • pressure waves • Intensity decreases with square of distance (for spherical waves) • speed of sound in air v(T) = (331.5+.6*T) T in celsius • Human hearing: 20Hz to 20,000 Hz • subsonic: frequencies below 20 Hz • ultra sonic: frequencies above 20,000 Hz • Intensity  Loudness • frequency  pitch • Example: A loudspeaker on a tall pole standing in a field generates a high frequency sound at an intensity of 1E-5 W/m2 for someone directly below the speaker whose ears are 8 m from the speaker. How loud is the sound when the person is 24 m from the speaker?

  10. Sound Levels • Human hearing can detect a wide range of intensities • Standard Scale: decibels (dB), a logarithmic scale • I0 = 1E-12 W/m2 , “Barely audible” • human hearing is not uniform, most sensitive from 2000-5000 Hz • 20 dB increase in L means 100x in intensity, 3dB change means 2x • 0 dB is barely audible, not 0 Intensity! • Pain at about 120 dB

  11. Doppler Effect • Motion of source or detector can affect measured frequency • Stationary Source, Observer • Moving Source, Stationary Observer • Stationary Source, Moving Observer

  12. Example: A police car emits a 250 Hz tone when sitting still. What frequency does a stationary observer hear if the car sounds it horn while approaching at a speed of 27 m/s? What frequency is hear if the horn is sounded as the car is leaving at 27 m/s? What sound is heard if the police car is stationary, but the observer is approaching/receding at 27 m/s?

  13. Beat Frequency • effect of superimposing two “close” frequencies

  14. Standing Waves II pipe open at one end 5l = 4L l = 4L 3l = 4L 7l = 4L node node antinode antinode

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