Tute W3 : SOUND 1. n = 10 log 10 I 2

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1 Tute W3 : SOUND 1 Some phenomena in nature can vary over an extremely large range of intensities and so it is convenient to define a logarithmic scale to describe them. An example is earthquakes, that are measured on a (logarithmic) Richter scale. Another example is our hearing since the human ear can detect a surprisingly large range of sound intensities. The logarithmic equation defining the difference in level between any two sound intensities I 1 and I 2 is ( ) I1 n = 10 log 10 I 2 where the unit for n is decibels (db). Acoustic power from a sound source is a measure of emitted sonic energy E per time t unit : where the unit for P is watts (W). P = IA = I(4πr 2 ) 1. If a sound level I 1 is 5 db louder than a sound level I 2, how many times more intense is I 1 compared with I 2? [ Answer: I 1 = 3.16 I 2 ] 2. If a sound level I 1 is 2 db less than a sound level I 2, how many times more intense is I 2 compared with I 1? [ Answer: I 2 = 1.58 I 1 ] 3. In a public address system, the input sound intensity at the microphone is known to be W m 2 and the output intensity at the speaker is W m 2. Find the decibel gain of the overall system. 1 April 12,

2 [ Answer: 53 db ] In order to establish an absolute sound level scale, comparisons are made with a fixed minimum sound level which is taken to be the smallest discernible sound. The threshold of hearing has an intensity I 0 = W m 2 and so the decibel scale can be defined as db level = 10 log 10 ( I I 0 ) where I is the intensity of the required sound and I 0 is the threshold of hearing. 4. The threshold of pain is the sound level which can rupture the eardrum and occurs at 120 db. What sound intensity does this correspond to? [ Answer: I = 1 W m 2 ] 5. Calculate the sound level of a sound wave that has an intensity of 4 µw m 2. [ Answer: 66 db ] 6. A vacuum cleaner has a sound level of 70 db. What is the sound intensity in W m 2? [ Answer: 10 5 W m 2 ] 7. A sound level of 50 db (such as a person talking) is added to another sound with a level of 70 db (such as a vacuum cleaner). What is the total sound level in decibels? [ Answer: db ] 2

3 8. A whispering FSC student possesses a sound level of 45 db. If a physics tutorial consists of 25 whispering students, what is the total decibel level the patient tutor has to endure? Assume each inconsiderate student produces the same sound level. [ Answer: 59 db ] 9. The AFL grand final is being played at the MCG and has an attendance of 92,551. During the game a Richmond player takes a fantastic mark and all the spectators cheer out loudly. If each cheering person in the crowd creates an average sound level of 50 db as heard by a player on the field, what total sound level in db does a player hear from the whole crowd? [ Answer: 99.7 db (an enormous roar!) ] 10. An FSC physics student is sitting 3 m from a speaker at a heavy metal concert. The sound level where the student is sitting is 120 db (the threshold of pain). How far from the speaker would the student have to move so that the sound level drops to (a) 100 db (loud mower)? (b) 50 db (normal conversation)? (c) 0 db (threshold of hearing)? [ Answer: (a) 30 m (b) 9.5 km (c) 3000 km ] 11. A point source emits sound waves with a power output of 55 W. (a) Calculate the intensity of the sound at a distance of 4 m from the source both in units of W m 2 and db. (b) Find the distance at which the sound reduces to a level of 70 db. [ Answer: (a) W m 2 ; db (b) 662 m ] 3

4 12. A noisy dog belonging to your neighbour barks with a power output of 78.5 mw. (a) What is the sound level in both W m 2 and db from your backyard which is 10 m from the barking dog? (b) How far away would the barking dog have to be so that its sound level is the same as normal conversation? (c) How far away would the barking dog have to be in order to be unheard? [ Answer: (a) 62.5 µw m 2 or 78 db (b) 250 m (c) 79 km! ] 13. At peak period the sound level on a busy motorway is 80 db, when 100 cars pass per minute. Find the sound level (in db) later in the evening when the number of cars passing per minute has fallen to 10. [ Answer: 70 db ] 14. The sound level experienced by a person standing near a noise generator is 70 db. What is the corresponding sound intensity? The noise generator is now turned up so that it produces five times the acoustic power. What is the new intensity and corresponding sound level in db experienced by the above person? [ Answer: I = 10 5 W m 2 ; I new = W m 2 ; 77 db ] 15. A mosquito has an average sound level of 25 db when flying 30 cm from your ear. (a) What is the acoustic power of this mosquito? (b) What is the minimum distance d of the mosquito in order for you not to be able to hear it? (c) What is the sound level in db of the mosquito when flying 5 cm from your ear? (d) At a distance of 30 cm, how many flying mosquitos are needed to generate a sound level of 50 db (the average sound level of normal human conversation)? [ Answer: (a) P = 358 pw (b) d 5.3 m (c) 40.6 db (d) mosquitos ] 4

5 Further Practice Problems: 1. A small circular-shaped stereo speaker releases 1200 J of sound over 24-hr period. If the diameter of the circular speaker is 5 cm, what is the sound intensity level at the speaker? [ Answer: db ] 2. Blue whales are the loudest creatures; they can emit sound waves with an intensity of W/m 2. If this intensity is measured 4.0 m from its source, what power is associated with the sound wave? [ Answer: 0.6 W ] 3. In 1983, Roy Lomas became the worlds loudest whistler; the power of his whistle was W. What was the sounds intensity at 2.5 m? [ Answer: db ] 4. Howler monkeys, found in Central and South America, can emit a sound that can be heard by a human several miles away. The power associated with the sound is roughly W. If the threshold of hearing of a human is assumed to be W/m 2, how far away can a howler monkey be heard. [ Answer: m ] 5. In 1988, Simon Robinson produced a sound having an intensity level of W/m 2 at a distance of 2.5 m. What power was associated with Robinsons scream? [ Answer: W ] 6. How much power is given off as sound from a gasoline-powered air compressor if the intensity of the sound is W/m 2 at a distance of 18 m? 5

7. A baseball coach shouts loudly at an umpire standing 5.0 m away. If the sound power produced by the coach is 3.1 10 3 W, what is the decibel level of the sound when it reaches the umpire?

6 7. A baseball coach shouts loudly at an umpire standing 5.0 m away. If the sound power produced by the coach is W, what is the decibel level of the sound when it reaches the umpire? [ Answer: db ] 8. Henry and Tom see a flash of lightning and then hear the resulting clap of thunder. Henry measures the sound level of the thunder as 65 db while Tom, who is 800 m further from the event, measures it as 63 db. [ Answer: 3089 m ] 9. A ten-year exposure to the sound of a riveting machine will cause your threshhold of hearing to shift from 0 db to 30 db. What is the sound intensity corresponding to 30 db? The normal lowest detectable intensity is W/m The area of a typical eardrum is about m 2. Calculate the sound power incident on an eardrum at (a) the threshold of hearing (b) the threshold of pain. [ Answer: P = W ; P = W ] 11. Two small speakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.00 mw, and speaker B has an output of 1.50 mw. Determine the sound level (in decibels) at point C in the Figure below assuming (a) only speaker A emits sound, (b) only speaker B emits sound, and (c) both speakers emit sound. [ Answer: 65 db ; 67.8 db ] 6

7 12. A fireworks rocket explodes at a height of 100 m above the ground. An observer on the ground directly under the explosion experiences an average sound intensity of W/m 2 for s. (a) What is the total sound energy of the explosion? (b) What is the sound level (in decibels) heard by the observer? [ Answer: 1.76 kj ; 108 db ] 7

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