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

Use the formula: 
L1/L2 = (d2/d1)^2 
where L1 is the loudness at distance d1, L2 is the loudness at distance d2. 
Substituting in the given values: 
60/L2 = (7/4)^2 
L2 = 60/(49/16) 
L2 = 9.8 dB (rounded to the nearest tenth) 
Therefore, the hair dryer is 9.8 dB loud for a person 7 feet away, which is closest to option B (19.6 dB is double of 9.8 dB).

The Loudness of a Sound (Measured in Decibels DB)