The decibel level of an orchestra is 90 dB, and a single violin achieves a level of 70 dB. How d

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The decibel level of an orchestra is 90 dB, and a single...

The decibel level of an orchestra is $90 \mathrm{dB}$, and a single violin achieves a level of $70 \mathrm{dB}$. How do the intensity and volume of the sound of the full orchestra compare with those of the violin's sound?

Key Concepts

Decibel Scale

The decibel (dB) is a logarithmic unit used to quantify sound intensity. This means that even small differences in decibel values represent significant differences in the actual energy or power of the sound. The scale compresses the wide range of sound intensities into a manageable numerical range, making it easier to compare sounds that vary in magnitude by many orders.

Logarithmic Scale

The decibel scale is logarithmic, which implies that each 10 dB increase corresponds to a tenfold increase in sound intensity. This characteristic allows for the representation of sound levels that differ drastically in magnitude in a compact and meaningful way.

Sound Intensity

Sound intensity is a physical measure of the power of a sound wave per unit area. It is closely related to the perceived loudness of a sound and is typically measured in watts per square meter. The relationship between sound intensity and decibel level is exponential, meaning that a small change in decibels can result in a large change in actual intensity.

Intensity Ratio Calculation

To compare sound intensities when given in decibels, one uses the formula I?/I? = 10^((dB? - dB?)/10). This formula directly relates the difference in decibel levels to a multiplicative factor in sound intensity, clearly demonstrating how a given decibel difference translates into a significant difference in physical energy.

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