Question

[2] Explain why we use a logarithmic decibel scale instead of Pascals when discussing the energy n sound waves E. F. [ Sound intensity & sound intensity level - Watch units! a. [0.5] Determine the sound intensity level of a sound whose intensity is 0.0051 W/m2 b. [0.5] Determine the sound intensity of a sound whose sound intensity level is 72 dB (re: 10-12 W/m2). G. Sound power & sound power level - Watch units! a. [0.5] Determine the sound power of a sound whose sound power level is 91 dB (re: 10-12 W) b. [0.5] Determine the sound power level of a sound whose sound power is 1.2 x 10 w.

Answer 1

E.We use logarithmic decibel , because the logarithmic nature makes it possible to express a wide range of sound intensities with a small range of numbers.

F. Sound Intensity and Sound Intensity Level:

Sound Intensity- It is defined as Sound Power per unit Area.The basic units are watt/m² or watts /cm² .The Intensity of the faintest sound that is audible is called the Threshold of Hearing.This has an intensity of about 1 * 10^-12 Wm^-2.

Sound Intensity Level- It tells us the level of Sound relative to a reference intensity expressed in decibels.

(a) Given, Sound Intensity (I) = 0.0051 Wm^-2

Reference Sound Intensity (I₀) = 10^-12 Wm^-2

We need to find - Sound Intensity Level (LI)

$L_{I} = 10 log_{10}(\frac{I}{I_{0}}) dB$

$L_{I} = 10 log_{10}(\frac{51 \times 10^{-4}}{10^{-12}}) dB$

$L_{I} = 10 log_{10}(51 \times 10^{8}) dB$

$L_{I} = 10 [log_{10}(51) + 8log_{10}10 ] dB$

$L_{I} = 10 [1.707 + 8 ] dB$

$L_{I} = 10 [9.707 ] dB$

$L_{I} = 97.07 dB$

(b) Given, Sound Intensity level = 72 dB

Reference Sound Intensity (I₀) = 10^-12 Wm^-2

We need to find Sound Intensity

I = I₀ 10^L_I/10 Wm^-2

I = 10^-12 * 10^72/10 Wm^-2

I= 10^-12 * 10^36/5 Wm^-2 = 10^-12 * 10^7+1/5 Wm^-2 ........ ( 36/5 expressed in mixed fractions)

I = ​​10^-12 * 10⁷ * 10^1/5 Wm^-2

I = 1.5 * 10^-5 = 0.000015 Wm^-2

G. Sound Power & Sound Power Level-

Sound Power- It is the rate at which sound energy is emitted , per unit time Or, The total energy emitted by a source per unit time is the Sound Power.. The S.I Unit is Watt.

Sound Power Level- It is the logarithmic measure of the power of a sound relative to the reference value. Sound Power Level is indicated in decibels. The Reference Power is 10^-12 W, which is the lowest sound persons of excellent hearing can identify.

G - (a) & (b) are solved in the below image