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Question 11 Mark

If the intensity of sound is doubled, by how many decibels does the sound level increase?

Answer

We know that, $\beta=10\log_{10}\frac{\text{J}}{\text{I}_0}$ According to the questions$\beta_\text{A}=10\log_{10}\Big(\frac{2\text{I}}{\text{I}_0}\Big)$
$\Rightarrow\beta_\text{B}-\beta_\text{A}=10\log\Big(\frac{2\text{I}}{\text{I}}\Big)$
$=10\times0.3010$
$=3\text{dB}.$

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Question 21 Mark

A Kundt's tube apparatus has a copper rod of length 1.0m clamped at 25cm from one of the ends. The tube contains air in which the speed of sound is 340m/s. The powder collects in heaps separated by a distance of 5.0cm. Find the speed of sound waves in copper.

Answer

$\text{V}_\text{rod}=?,\ \text{V}_\text{air}=340\text{m/s},$$\text{L}_\text{r}=25\times10^{-2},\ \text{d}_2=5\times10^{-2}\ \text{meters}$
$\frac{\text{V}_\text{r}}{\text{V}_\text{a}}=\frac{2\text{L}_\text{r}}{\text{D}_\text{a}}$
$\Rightarrow\text{V}_\text{r}=\frac{340\times25\times10^{-2}\times 2}{5\times10^{2}}$
$\Rightarrow \text{V}_{\text{rod}}=3400\text{m/s}$

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