At a given frequency, it is possible to discern differences of about 1 dB, and a change of 3 dB is easily noticed. The perception of intensity is called loudness. Musical notes are sounds of a particular frequency that can be produced by most instruments and in Western music have particular names, such as A-sharp, C, or E-flat. For example, 500.0 and 501.5 Hz are noticeably different. Typically, humans have excellent relative pitch and can discriminate between two sounds if their frequencies differ by 0.3% or more. The perception of frequency is called pitch. It can give us a wealth of simple information-such as pitch, loudness, and direction. The human ear has a tremendous range and sensitivity. It is beyond the scope of this text to treat this scale because it is not commonly used for sounds in air, but it is important to note that very different decibel levels may be encountered when sound pressure levels are quoted. This scale is used particularly in applications where sound travels in water. Identify common sounds at the levels of 10 dB, 50 dB, and 100 dB.Īnother decibel scale is also in use, called the sound pressure level, based on the ratio of the pressure amplitude to a reference pressure. Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than 10 −9 atm. The ear is sensitive to as little as a trillionth of a watt per meter squared-even more impressive when you realize that the area of the eardrum is only about 1 cm 2, 1 cm 2, so that only 10 −16 W 10 −16 W falls on it at the threshold of hearing. Table 17.2 gives levels in decibels and intensities in watts per meter squared for some familiar sounds. The decibel level of a sound having the threshold intensity of 10 −12 W/m 2 10 −12 W/m 2 is β = 0 dB, β = 0 dB, because log 10 1 = 0. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone. The units of decibels (dB) are used to indicate this ratio is multiplied by 10 in its definition. Because β β is defined in terms of a ratio, it is a unitless quantity, telling you the level of the sound relative to a fixed standard ( 10 −12 W/m 2 10 −12 W/m 2). How human ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly by the intensity. It is more common to consider sound intensity levels in dB than in W/m 2. Where I 0 = 10 −12 W/m 2 I 0 = 10 −12 W/m 2 is a reference intensity, corresponding to the threshold intensity of sound that a person with normal hearing can perceive at a frequency of 1.00 kHz. Figure 17.14 shows the anatomy of the ear.

The ear is a transducer that converts sound waves into electrical nerve impulses in a manner much more sophisticated than, but analogous to, a microphone. The sound wave that impinges upon our ear is a pressure wave. The hearing mechanism involves some interesting physics.

Human Hearing and Sound Intensity LevelsĪs stated earlier in this chapter, hearing is the perception of sound.

This relationship is consistent with the fact that the sound wave is produced by some vibration the greater its pressure amplitude, the more the air is compressed in the sound it creates. The pressure variation is proportional to the amplitude of the oscillation, so I varies as ( Δ p ) 2. In this equation, ρ ρ is the density of the material in which the sound wave travels, in units of kg/m 3, kg/m 3, and v is the speed of sound in the medium, in units of m/s. The energy (as kinetic energy 1 2 m v 2 1 2 m v 2) of an oscillating element of air due to a traveling sound wave is proportional to its amplitude squared. Here, Δ p max Δ p max is the pressure variation or pressure amplitude in units of pascals (Pa) or N/m 2 N/m 2.

Intensity equation