The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x)=10log(frac{x}{10}), wh

texelaare

texelaare

Answered question

2021-01-28

The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x)=10log(x10), where I0=1012 watt per square meter is the least intense sound that a human ear can detected. Determine the loudness, in decibels, of each of the following sounds.
Heavy city traffic: intensity of x=103 watt per square meter.

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-01-29Added 169 answers

It is observed that the loudness is a logarithmic function. Hence, the different properties of logarithmic function can be used to find the find the intensity. The different properties of the logarithmic function are found from the properties of the exponential functions as exponential functions are inverse functions of logarithmic functions.
Now, to find the intensity at x=103 watt per sq meter, substitute this value in the loudness function given by L(x).The logarithmic properties log(xn)=nlog(x) and log(10)=1 can be used simplify the equation.
L(x)=10log(x10)
L(103)=10log(10310)
=10log(102)
=2×10log(102)
=2×10log(10)
=2×10
=20 dB

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