What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20 dB.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Decibel rating for sound is calculated by taking 10 multiplying by the logarithm of the intensity divided by some reference intensity at the threshold of hearing. So, we can divide both sides by 10. And that gives log I for I naught equals decibels divided by 10. And then raise both sides to the power of 10 or make both sides powers of 10 I guess I should say. So that makes the left hand side I over I naught and on the right hand side we have 10 to the power of beta over 10. So, multiply both sides by I naught. And you get the intensity is the reference intensity times 10 to the power of decibels over 10. So, for the pain threshold intensity, we have 1.0 times 10 to the minus 12 watts per meter squared reference intensity at the threshold of hearing times by 10 to the power of 120 decibels over 10. And that gives 1.0 watts per square meter. And the intensity of a whisper is 1.0 times 10 to the minus 12 watts per square meter times 10 to the power of 20 decibels over 10 which gives 1.0 times 10 to the minus 10 watts per square meter. So, the difference between them is enormous. So, if you find the factor by which they're different, you can take intensity for the pain threshold divided by intensity for the whisper and that's 1.0 / 1.0 times 10 to the minus 10 and that gives 10 to the power of 10. So, the intensity of the sound at the pain threshold is 10 to the 10 times more intense than the intensity of the whisper.