Halliday, Resnick & Walker — Waves–II: Problem 110

The most common handgun carried by United States police officers is the Glock 22 (0.40 caliber). The officers must qualify and train with the weapon on firing ranges where hearing protection is required to avoid hearing loss, possibly permanent loss. In one investigation of the protection, a Glock 22 was fired 1.0 m from a mannequin. The noise was detected by two microphones. One was under protective gear on the mannequin’s ear and one was adjacent to the mannequin and unprotected. The noise level was measured in terms of the sound pressure level SPL (units dB SPL), which is defined as \(SPL = 20 \log(p/p_0)\), where \(p\) is the measured sound pressure and \(p_0\) is the reference pressure of \(20\ \mu\text{Pa}\ (= 20\ \mu\text{N/m}^2)\). What were the pressures for (a) 158 dB SPL for the unprotected microphone, (b) 123 dB SPL for the mannequin with the protective earmuffs, and (c) 103 dB SPL for the mannequin with both earmuffs and earplugs? The recommended allowable exposure set by the National Institute for Occupational Safety and Health is 140 dB SPL, which would be exceeded by an officer firing a Glock 22 without protection, as is sometimes required in the line of duty.