The loudness of a sound (measured in decibels dB) is inversely proportional to the square of the distance from the source of the sound. Suppose a person who is 4 ft from a hair dryer experiences a sound level of 60 dB. How loud is the hair dryer for a person 7 ft away? Round to the nearest tenth.
A) 0.1 dB
B) 19.6 dB
C) 1.2 dB
D) 70.0 dB
E) 960.0 dB

Question

The loudness  of a sound (measured in decibels dB) is inversely proportional to the square of the distance  from the source of the sound. Suppose a person who is 4 ft from a hair dryer experiences a sound level of 60 dB. How loud is the hair dryer for a person 7 ft away? Round to the nearest tenth.
A) 0.1 dB 
B) 19.6 dB 
C) 1.2 dB 
D) 70.0 dB 
E) 960.0 dB

Quizplus · Accepted Answer

Using the inverse square law formula: 
L1/L2 = (r2/r1)^2
where L1 is the initial loudness (60 dB) and r1 is the initial distance (4 ft), and L2 is the loudness we are trying to find and r2 is the new distance (7 ft).
Substituting: 
60/L2 = (7/4)^2
60/L2 = 3.06
L2 = 19.6 dB (rounded to the nearest tenth)

The Loudness of a Sound (Measured in Decibels DB)