Hearing damage may occur when a person is exposed to a sound...

Hearing damage may occur when a person is exposed to a sound intensity level of $90.0 \mathrm{~dB}$ (relative to the threshold of hearing) for a period of $9.0$ hours. One particular eardrum has an area of $2.0 \times 10^{-4} \mathrm{~m}^{2}$. How much sound energy is incident on this eardrum during this time?

Key Concepts

Time Integration

Time integration in the context of sound energy involves accumulating the energy delivered over a period of time. By multiplying the instantaneous sound intensity by the duration of exposure, one can calculate the total energy incident on a surface. This concept is essential when considering exposure durations in applications such as assessing hearing risk or acoustic energy transfer.

Sound Energy

Sound energy is the total amount of energy carried by sound waves as they interact with a surface. It can be calculated by multiplying the sound intensity by the area over which the sound is being received and by the time duration of exposure. This integration of intensity over an area and a time period yields the total energy imparted, which is crucial in assessing potential damage or energy transfer.

Sound Intensity

Sound intensity refers to the power carried by sound waves per unit area. It is a measure of the energy transmitted by the wave and is typically defined as the power per unit area, measured in watts per square meter. When solving problems involving sound, intensity is a key link between the abstract measurement of sound (in decibels) and the concrete calculation of energy impacting a surface.

Decibel Scale

The decibel (dB) scale is a logarithmic scale used to express the ratio of a given sound intensity to a reference intensity. It facilitates the wide range of sound intensities encountered in practice by converting multiplicative differences into additive differences. The relationship between decibels and intensity typically involves the formula I = I? × 10^(L/10), where I? is the reference intensity and L is the sound level in decibels.

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