The amount of time required to produce permanent damage to hearing is cut in half with an increase in sound of:

The correct answer is based on the principles of sound intensity and its relation to the risk of hearing damage. An increase in sound levels is measured in decibels (dB), which follows a logarithmic scale. Specifically, an increase of approximately 3 dB represents a doubling of the sound intensity. This relationship is critical when considering the effects of sound on hearing over time.

When sound levels are increased by around 3 dB, the intensity doubles, and research indicates that this increase can cut the time required for hearing damage in half. As the sound pressure level rises, the risk of permanent hearing damage increases exponentially, meaning even small increases in dB can significantly impact the duration of safe exposure.

Hence, an increase of 5 dB would result in more than just halving the time; it represents a substantial rise in intensity and further reduces the safety time. Similarly, higher increases of 7 dB and 9 dB ensure even harsher conditions for auditory safety, leading to even shorter exposure times before damage occurs. Therefore, the increase of 3 dB is the precise threshold where the time to produce permanent hearing damage is halved, making this the foundational understanding in the context of sound exposure and hearing conservation.