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Sound and waves

Sound and waves. Sound waves. As the tuning fork vibrates, a succession of compressions and rarefactions of the air density are produced and propagate away from the fork A sinusoidal curve can be used to represent the longitudinal wave

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Sound and waves

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  1. Sound and waves PHY231

  2. Sound waves • As the tuning fork vibrates, a succession of compressions and rarefactions of the air density are produced and propagate away from the fork • A sinusoidal curve can be used to represent the longitudinal wave • Crests correspond to compressions and troughs to rarefactions • The sound is a longitudinal wave because the vibrations (here compression or rarefaction of air density) are in the same direction as the direction of propagation PHY231

  3. Types of sound waves • Audible waves • Lay within the normal range of hearing of the human ear • Normally between 20 Hz to 20,000 Hz • Infrasonic waves • Frequencies are below the audible range • Earthquakes are an example • Ultrasonic waves • Frequencies are above the audible range • Dog whistles are an example PHY231

  4. wavelength • If the speed of propagation of the wave is v and its frequency f, the distance between consecutive maxima is called wavelength and usually noted l (lambda): PHY231

  5. Applications of ultrasounds • Ultrasonic waves f>20 kHz (in air l<2 cm) • Can be used to produce images of small objects • Many Applications uses the reflection of the ultrasonic wave as a locating/imaging tool • Ultrasounds to observe babies in the womb • Ultrasonic ranging unit for cameras • SONAR PHY231

  6. Sound waves • Which of the following ranges corresponds to the longest wavelengths? • A) infrasonic • B) audible • C) ultrasonic • D) all have the same wavelengths PHY231

  7. Sound waves • Which of the following ranges corresponds to the longest wavelengths? • A) infrasonic • B) audible • C) ultrasonic • D) all have the same wavelengths PHY231

  8. Wavelength • The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz. What wavelength is associated with this frequency? (Assume the speed of sound to be 340 m/s.) • A) 1.7 cm • B) 5.2 cm • C) 34 cm • D) 55 cm PHY231

  9. Wavelength • The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz. What wavelength is associated with this frequency? (Assume the speed of sound to be 340 m/s.) • A) 1.7 cm • B) 5.2 cm • C) 34 cm • D) 55 cm PHY231

  10. Intensity of sound wave • As a sound wave propagates, it carries energy • The rate of energy transfer by second and by unit area is the intensity I • The area A is perpendicular to the direction of the energy flow • For human ears: • Threshold of hearing I ~10-12 W/m2 • Threshold of pain I ~1 W/m2 PHY231

  11. Intensity levels in Decibels • The human ear is functional over twelve order of magnitudes of intensity • Our perception of the intensity however is not linear but logarithmic. For this reason, a logarithmic unit system, the decibels, is defined as • I0=10-12 W/m2 is the threshold of hearing • b in decibels = dB PHY231

  12. Intensity levels in Decibels Multiplying the intensity by: factor 10 means increasing by 10dB factor 100 means increasing by 20dB etc… Dividing the intensity by: factor 10 means decreasing by 10dB factor 100 means decreasing by 20dB etc… I (W/m2) b (dB) Threshold of hearing I=10-12 W/m2 Threshold Of pain I = 1W/m2 b (dB) I (W/m2)

  13. How loud? • Which of the following best describes a sound level of intensity 1 W/m2? • A) extremely loud • B) about that of a power mower • C) normal conversation • D) like a whisper PHY231

  14. How loud? • Which of the following best describes a sound level of intensity 1 W/m2? • A) extremely loud • B) about that of a power mower • C) normal conversation • D) like a whisper PHY231

  15. Intensity • Tripling the power output from a speaker emitting a single frequency will result in what increase in loudness? • A) 0.33 dB • B) 3.0 dB • C) 4.8 dB • D) 9.0 dB PHY231

  16. Intensity • Tripling the power output from a speaker emitting a single frequency will result in what increase in loudness? • A) 0.33 dB • B) 3.0 dB • C) 4.8 dB • D) 9.0 dB PHY231

  17. Spherical sound waves • A source-sphere contracting and expanding periodically will generate a spherical sound wave • The disturbance moves away from the source on a spherical wave front • The wavelength l is the distance between consecutive wave fronts PHY231

  18. Intensity for spherical waves • The spherical wave front expands in radial direction • At a radius r from the source • For example: 2m away from the source, the intensity is 4 times smaller than at 1m away • Power crossing each surface is the same but the intensity decreases with the distance • The amplitude of the wave is the square-root of the intensity

  19. Plane waves • Plane waves have Wavefronts that are parallel to each other and moving on a straight line • Such a situation can arise for example at very large distance from the source of a spherical wave source (>>l) PHY231

  20. dB for spherical waves • If the distance between a point sound source and a dB detector is increased by a factor of 4, what will be the reduction in intensity level? • A) 16 dB • B) 12 dB • C) 4 dB • D) 0.5 dB PHY231

  21. dB for spherical waves • If the distance between a point sound source and a dB detector is increased by a factor of 4, what will be the reduction in intensity level? • A) 16 dB • B) 12 dB • C) 4 dB • D) 0.5 dB PHY231

  22. Jet airliner altitude • The intensity level of sound 20 m from a jet airliner is 120 dB. At what distance from the airplane will the sound intensity level be a tolerable 100 dB? (Assume spherical spreading of sound.) • A) 90 m • B) 120 m • C) 150 m • D) 200 m PHY231

  23. A) 90 m • B) 120 m • C) 150 m • D) 200 m PHY231

  24. Solar power on earth • The sun’s surface temperature is about 5800 K, its radius 7.0x108 m and its emissivity 0.97. Assuming the distance of the earth to the sun is about 1.5x1011 m, what is the intensity received on earth from the sun? (s=5.67x10-8 W/m2/K4) • A) 1.4 W/m2 • B) 14 W/m2 • C) 0.14 kW/m2 • D) 1.4 kW/m2 PHY231

  25. Solar power on earth earth Distance sun-earth A) 1.4 W/m2 B) 14 W/m2 C) 0.14 kW/m2 D) 1.4 kW/m2 sun PHY231

  26. Doppler effect • The frequency detected by an observer varies if observer and/or source move • Higher frequency when source and observer move toward each other. Lower frequency when they move away from each other • End result (general case) fo : Freq. measured by the observer fs : Freq. emitted by the source v : speed of propagation for wave vo : observer velocity in the medium vs : source velocity in the medium !!! v0>0 when pointing toward source (<0 otherwise) !!! vs>0 when pointing toward observer (<0 otherwise)

  27. Wavelength illustration • Wavelength of the wavefront travelling with the moving source is shortened • Wavelength of the wavefront travelling opposite to the moving source is lengthened lwm Frequency doesn’t change in the direction perpendicular to the motion source doesn’t move lwm lwm source moves l- < lwm (frequency increases) l+ > lwm (frequency decreases) l same everywhere

  28. If observer moves • 1) Example showing how formula simplifies (works for all cases) Observer moves toward wave front He will have impression the wavelength is even smaller (i.e. higher frequency) PHY231

  29. Train • A train station bell gives off a fundamental tone of 500 Hz as the train approaches the station at a speed of 20 m/s. If the speed of sound in air is 335 m/s, what will be the apparent frequency of the bell to an observer riding the train? • A) 532 Hz • B) 530 Hz • C) 470 Hz • D) 472 Hz PHY231

  30. Train • A train station bell gives off a fundamental tone of 500 Hz as the train approaches the station at a speed of 20 m/s. If the speed of sound in air is 335 m/s, what will be the apparent frequency of the bell to an observer riding the train? • A) 532 Hz • B) 530 Hz • C) 470 Hz • D) 472 Hz PHY231

  31. Train • You stand by the railroad tracks as a train passes by. You hear a 1 000-Hz frequency when the train approaches, which changes to 800 Hz as it goes away. How fast is the train moving? The speed of sound in air is 340 m/s. • A) 15.7 m/s • B) 21.2 m/s • C) 28.0 m/s • D) 37.8 m/s PHY231

  32. Train • A) 15.7 m/s • B) 21.2 m/s • C) 28.0 m/s • D) 37.8 m/s PHY231

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