Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. The Sacramento City Council adopted a law to reduce the allowed sound intensity level of the much-despised leaf blowers from their current level of about 95 dB to 70 dB. With the new law, what is the ratio of the new allowed intensity to the previously allowed intensity?

Solution 16E Initial sound intensity level = 95 dB 1 Final sound intensity level = 70 d2 We know that sound intensity level is given by = (10 dB)log I I 0 Therefore, 95 dB = (10 dB)log I1 …..(1) I0 Here, I is1the initial sound intensity. If I i2 the final sound intensity, I 2 70 dB = (10 dB)log I 0…..(2) Now, subtracting equation (2) from equation (1), 95 70 dB = 10 dBlog I 1 I 2 25 dB = 10 dBlog I 1 I 2 I log 1 = 2.5 I 2 2.5 I 1 = I 20 I = 10 2.5I 2 1 2.5 I 2I 1 = 10 I 2I 1 = 0.0032 I /I = 3.20 × 10 3 2 1 Therefore, the ratio of the new allowed intensity to the previously allowed intensity is 3.20 × 10 3 : 1.