Question

An increase in the intensity level of one decibel implies an increase in intensity of :

• A. $1\text{\%}$
• B. $3.01\text{\%}$
• C. $26\text{\%}$
• D. $0.1\text{\%}$

Answer 1

The correct option is C $26\text{\%}$

The Decibel scale is given by
L = $10log\left(\frac{I}{I{}_o}\right)$ ; $I{}_o$ is the intensity at threshold for hearing.
Let the reading be X;
X = $10log\left(\frac{I{}_1}{I{}_0}\right)$;
X + 1 = $10log\left(\frac{I{}_2}{I{}_0}\right)$;
Subtracting the equations we get
$\Rightarrow$1 = 10($log\frac{I{}_2}{I{}_0}-log\frac{I{}_1}{I{}_0}$)
$\Rightarrow$1 = 10($log\frac{I{}_2}{I{}_1}$)
$\Rightarrow$$log\frac{I{}_2}{I{}_1}$ = $\frac{1}{10}$
$\Rightarrow$$\frac{I{}_2}{I{}_1}$ = ${10}^{0.1}$ ; ${10}^{0.1}$ = 1.26;
$\Rightarrow$$\frac{I{}_2}{I{}_1}$ = 1.26;
$\Rightarrow$$I{}_2$=1.26$I{}_1$; And hence a 26% increase