If you know the sound level in decibels at one distance in an open area, then you can estimate the dB level at another distance by making use of the inverse square law.Ī useful general reference is that the just noticeable difference in sound intensity for the human ear is about 1 decibel. Then the difference in decibels is given by I A = dB above I B If one is expressed as a multiple of the other: I A = x I B = x 10^ x I B Then the intensity in decibels is given byĭecibels can also be used to express the relative intensity of two sounds. If the intensity as a multiple of threshold is The sound intensity in decibels above the standard threshold of hearing is calculated as a logarithm. The logarithm to the base 10 used in this expression is just the power of 10 of the quantity in brackets according to the basic definition of the logarithm: The decibel scale is a reflection of the logarithmic response of the human ear to changes in sound intensity: The unit is based on powers of 10 to give a manageable range of numbers to encompass the wide range of the human hearing response, from the standard threshold of hearing at 1000 Hz to the threshold of pain at some ten trillion times that intensity.Īnother consideration which prompts the use of powers of 10 for sound measurement is the rule of thumb for loudness: it takes about 10 times the intensity to sound twice as loud. The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because about 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear.ĭecibels provide a relative measure of sound intensity. Example: If I = 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 10 4, the power of ten is 4, and the intensity is 40 dB: The logarithm involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. To calculate this result, we must compare the intensities in watt/m 2.The sound intensity I may be expressed in decibels above the standard threshold of hearing I 0. If the speaker is assumed to be a point source, how far from the speaker will the sound have intensity levels of (a)Ħ0 dB and (b) just barely enough to be heard? A 1000-hz tone issuing from a loudspeaker has a sound level intensity of 100 dB at a distance ofĢ. If the wall absorbs 20%, then 80% is reflected. 5 X 10 -4 W/m 2 Assuming that the wall absorbs 20% of the incident energy and reflects the rest, what is the sound intensity level just before and after the sound is reflected? 0 m from a wall shouts so that the sound strikes the wall with an intensity ofĢ. 5 x 10 -4 W/m 2 What is the difference in the average soundĤ3. 5 X 10 -6 W/m 2 and another movement is played fortissimo (very loudly) atĢ. An orchestra plays a movement pianissimo (very softly) at an average intensity ofħ. Since sound obeys an inverse square law, weĤ1. Intensities of each of the sound level readings. To determine this answer, we must first know the At what distanceįrom the source will the sound level intensity be 40 dB? 0 m from a point source, the sound intensity level is measured to be 70 dB. Therefore, 90 dB is 10 5 times louder than 40 dBģ9. To compare the intensity of these two decibel The sound intensity levels for a machine shop and a quiet library are 90 dB and 40 dB, respectively (a) How many times greater is the intensity of the sound in the machine shop than that in the office? (b) What is each intensity? Sound level intensity of 70 dB occurred when we were 3 meters from the speaker.ģ6. Now we can use our formula for power and the fact that the Watts/m 2, the threshold of human hearing So we must first convert decibels to watts/m 2 using the Represents the intensity in watt/m 2 not the sound level intensity inĭecibels. What is the approximate sound power emitted by the speaker? Sound from a loudspeaker, which approximates a point source, is measured to have a sound level intensity of 70 dB at a distance ofģ. Sound Level Intensity (Decibels) and Sound Intensity (W/m 2)ģ5. Set 11: Sound Level Intensity and Sound Intensity
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