SOLUTION (A) Calculate the intensity level of the single grinder. Substitute the intensity into the decibel...

Transcribed Image Text:

SOLUTION (A) Calculate the intensity level of the single grinder. Substitute the intensity into the decibel formula. (B) Calculate the new intensity level when an additional machine is added. Substitute twice the intensity of part (a) into the decibel formula. 2.00 x 10-5 W/m² 1.00 x 10-12 W/m² Substitute 77.0 dB into the decibel formula and divide both sides by 10. B = 10 log Make each side the exponent of 10. On the right-hand side, 10log(u) = u, by definition of base 10 logarithms. (C) Find the intensity corresponding to an intensity level of 77.0 dB. B = 77.0 dB = 10 log(I/Io) B = 10 log 1.00 x 10-5 W/m² 1.00 x 10-12 W/m² dB 7.70 = log I 10-12 W/m² 107.70 5.01 x 107 = I= 5.01 x 10-5 W/m² = 10 log(107) = 70.0 dB = 73.0 dB I 1.00 x 10-12 W/m² LEARN MORE REMARKS The answer is five times the intensity of the single grinder, so in part (c) there are five such machines operating simultaneously. Because of the logarithmic definition of intensity level, large changes in intensity correspond to small changes in intensity level. QUESTION By how many decibels is the sound intensity level raised when the sound intensity is doubled? SOLUTION (A) Calculate the intensity level of the single grinder. Substitute the intensity into the decibel formula. (B) Calculate the new intensity level when an additional machine is added. Substitute twice the intensity of part (a) into the decibel formula. 2.00 x 10-5 W/m² 1.00 x 10-12 W/m² Substitute 77.0 dB into the decibel formula and divide both sides by 10. B = 10 log Make each side the exponent of 10. On the right-hand side, 10log(u) = u, by definition of base 10 logarithms. (C) Find the intensity corresponding to an intensity level of 77.0 dB. B = 77.0 dB = 10 log(I/Io) B = 10 log 1.00 x 10-5 W/m² 1.00 x 10-12 W/m² dB 7.70 = log I 10-12 W/m² 107.70 5.01 x 107 = I= 5.01 x 10-5 W/m² = 10 log(107) = 70.0 dB = 73.0 dB I 1.00 x 10-12 W/m² LEARN MORE REMARKS The answer is five times the intensity of the single grinder, so in part (c) there are five such machines operating simultaneously. Because of the logarithmic definition of intensity level, large changes in intensity correspond to small changes in intensity level. QUESTION By how many decibels is the sound intensity level raised when the sound intensity is doubled?