Solved: The intensity level of sound, L measured in decibels (dB), is a function of the... [IB Mathematics Applications & Interpretation (Math AI)]

The intensity level of sound, L measured in decibels (dB), is a function of the soundintensity, S watts per square metre (W m−2). The intensity level is given by the following formula. L = 10 lo g 10 ( S × 10 12 ) , S≥ 0.

Question

SLPaper 1

The intensity level of sound, $L$ measured in decibels (dB), is a function of the soundintensity, $S$ watts per square metre (W m⁻²). The intensity level is given by the following formula.

$L = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)$ , $S$ ≥ 0.

An orchestra has a sound intensity of 6.4 × 10⁻³W m⁻² . Calculate the intensity level, $L$ of the orchestra.

[2]

Verified

Solution

$10\,{\text{lo}}{{\text{g}}_{10}}\left( {6.4 \times {{10}^{ - 3}} \times {{10}^{12}}} \right)$ (M1)

= 98.1(dB) (98.06179…) A1

[2 marks]

A rock concert has an intensity level of 112 dB. Find the sound intensity, $S$ .

[2]

Verified

Solution

$112 = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)$ (M1)

0.158 (W m⁻²) (0.158489… (W m⁻²)) A1

[2 marks]

The intensity level of sound, L measured in decibels (dB), is a function of the soundintensity, S watts per square metre (W m−2). The intensity level is given by the following formula. L = 10 lo g 10 ( S × 10 12 ) , S≥ 0.

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