Hearing and Decibel Scales

The outer ear directs sound along the ear canal to the eardrum. The ossicles transmit its motion to the oval window, coupling energy into fluid in the cochlea. Motion in the cochlea stimulates sensory receptors, producing nerve signals. The middle-ear mechanism helps couple sound between air and fluid, which otherwise have a large acoustic mismatch.

Sound intensity is power crossing unit area perpendicular to propagation, in W m⁻². For an unobstructed isotropic point source, intensity decreases as the inverse square of distance. Reflection, absorption and background noise can invalidate that simple model in a room.

A level in dB compares an intensity with a reference intensity. Here use $I_0=1.0\times10^{-12}$ W m⁻². Zero dB is this reference, not zero physical intensity. Increasing intensity tenfold adds 10 dB; doubling it adds about 3 dB.

For two sounds, subtract their dB levels to obtain the logarithm of their intensity ratio. Do not divide the dB values. A level of 60 dB does not mean six times the intensity of 10 dB.

Equal-loudness curves show the intensity level required at each frequency for the same perceived loudness. Hearing is relatively sensitive in the few-kilohertz region and less sensitive at very low frequencies. To construct such a curve, listeners compare test tones with a reference tone and adjust levels to judge equal loudness.

A dBA meter applies a frequency weighting intended to approximate aspects of human hearing sensitivity. An unweighted dB reading and dBA reading therefore need not match. Age-related loss often raises high-frequency thresholds; noise exposure can also change the frequency response. A raised threshold means a stronger sound is needed for detection, not that the sound source has become quieter.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.