Sound and waves PHY231 1 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 PHY231 of propagation 2 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 3 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 lambda v f PHY231 4 Applications of ultrasounds Ultrasonic waves f 20 kHz in air 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 5 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 6 Sound waves Which of the following ranges corresponds to the longest wavelengths v A infrasonic f B audible C ultrasonic D all have the same wavelengths PHY231 7 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 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 v f A 1 7 cm B 5 2 cm 340 3 C 34 cm 20 10 2 D 55 cm 1 7 10 m 1 7cm PHY231 9 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 Power P 1 E I area A A t 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 10 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 I 10log I0 10 I I0 10 I0 10 12 W m2 is the threshold of hearing in decibels dB PHY231 11 Intensity levels in Decibels I 10log I0 I W m2 dB 1E 14 20 1E 13 10 1E 12 0 1E 11 10 1 00E 10 20 1 00E 09 30 1 00E 08 40 1 00E 07 50 1 00E 06 60 1 00E 05 70 1 00E 04 80 1 00E 03 90 1 00E 02 100 1 00E 01 110 1 120 10 130 dB 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 Threshold of hearing I 10 12 W m2 Threshold Of pain I 1W m2 I W m2 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 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 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 15 Intensity Tripling the power output from a speaker emitting a single frequency will result in what increase in loudness Tripling the power triples the intensity I 10log I A 0 33 dB I 10log B 3 0 dB I 3 I C 4 8 dB 10log I D 9 0 dB initial initial 0 final final 0 initial 0 Iinitial 10log 3 10log I 0 4 8 dB initial PHY231 16 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 is the distance between consecutive wave fronts PHY231 17 Intensity for spherical waves The spherical wave front expands in radial direction Power crossing each surface is the same but the intensity decreases with the distance At a radius r from the source The amplitude of power P the wave is the I 2 square root of the area 4 r intensity For example 2m away from the source the intensity is 4 times smaller than at 1m away 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 PHY231 19 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 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 Intensity I Power Area Here the distance is increased by a factor 4 A 16 dB The area has increased by a factor 4 2 16 B 12 dB C 4 dB Thus the intensity has dropped by a factor 16 D 0 5 dB I I2 1 16 We need to calcultae in dB I2 1 1 2 10log 10log 12 dB 16 PHY231 I1 21 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 22 A 90 m B 120 m C 150 m D 200 m The reduction needs to be 20 dB This means intensity must decrease by a factor 100 I1 I 2 I1 10 I1 10 I1 10 100 But intensity Power Area So we need to be at a distance such that the area is 100 times larger …
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