Question

After a beam passes through $\mathbf{10}\mathbf{}\mathbf{cm}$ of tissue, what is the beam’s intensity as a fraction of its initial intensity from the transducer?

(a)$\mathbf{1}\mathbf{\times }{\mathbf{10}}^{-11}$; (b)$\mathbf{0}\mathbf{.}\mathbf{001}$; (c)$\mathbf{0}\mathbf{.}\mathbf{01}$; (d) $\mathbf{0}\mathbf{.}\mathbf{1}$

Short answer

The correct option is $d$.

Step-by-step solution

Given Data

The beam length within the tissue is- $10cm$

Sound Intensity

The energy carried by a sound wave per unit area, per second, perpendicular to the direction of propagation, is called intensity of sound. In units of dB the intensity of sound is given as-

$\mathbf{\beta }\mathbf{=}\mathbf{\left(}\mathbf{10}\mathbf{dB}\mathbf{\right)}\mathbf{log}\frac{I}{{\mathbf{I}}_0}$

Here,$\mathbf{I}$ is the sound intensity and${\mathbf{\text{I}}}_{\mathbf{O}}$ is the threshold intensity of the wave.

Calculate the fraction

In $10\mathrm{cm}$ inside a tissue, the intensity is

$\begin{array}{c}\beta =\frac{-100\text{\hspace{0.17em}dB}}{10}\\ =-10\text{\hspace{0.17em}dB}\end{array}$

Using this value, find the fraction of intensity

$\begin{array}{c}-10dB=10dB\log \frac{I}{I_0}\\ \log \frac{I}{I_0}=-1\\ \frac{I}{I_0}=0.1\end{array}$

Hence, the required fraction is $0.1$.