Q78PP - University Physics with Modern Physics

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)   $\mathbf{0}\mathbf{.}\mathbf{1}$

Step-by-Step Solution

Answer

The correct option is $d$.

Step 1: Given Data

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

Step 2: 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.

Step 3: 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  $0.1$ .