Physics - Sound Wave Question with Solution | TestHub

To find the change in volume, we first calculate the bulk modulus (B) using the speed of sound (v) and density ($\rho$): $B=\rho v^2$.

Given $\rho =800kg/{\mathrm{m}}^3$ and $v=1330m/s$,

$B=800\times (1330{)}^2=800\times 1768900=1.415\times 10^{9}N/{\mathrm{m}}^2$.

The bulk modulus is also defined as $B=-\frac{\Delta P}{\Delta V/V}$.

We are given $\Delta P=2\times 10^{5}N/{\mathrm{m}}^2$ and $V=1\mathrm{L}=10^{-3}{\mathrm{m}}^3$.

So, $\Delta V=-\frac{\Delta P\cdot V}{B}$.

$\Delta V=-\frac{(2\times 10^{5}N/{\mathrm{m}}^2)\times (10^{-3}{\mathrm{m}}^3)}{1.415\times 10^{9}N/{\mathrm{m}}^2}=-1.413\times 10^{-7}{\mathrm{m}}^3$.

Converting to cm³: $\Delta V=-1.413\times 10^{-7}\times (100{)}^3\mathrm{c}{\mathrm{m}}^3=-0.1413\mathrm{c}{\mathrm{m}}^3$.

The magnitude of the change in volume is $0.14\mathrm{c}{\mathrm{m}}^3$.

The final answer is $\boxed{0.14\mathrm{c}{\mathrm{m}}^3}$.