JEE PYQ: Waves And Sound Question 13
Question 13 - 2020 (05 Sep Shift 1)
Assume that the displacement ($s$) of air is proportional to the pressure difference ($\Delta p$) created by a sound wave. Displacement ($s$) further depends on the speed of sound ($v$), density of air ($\rho$) and the frequency ($f$). If $\Delta p \sim 10$ Pa, $v \sim 300$ m/s, $\rho \sim q$ kg/m$^3$ and $f \sim 1000$ Hz, then $s$ will be of the order of (take the multiplicative constant to be 1)
(1) $\frac{3}{100}$ mm
(2) 10 mm
(3) $\frac{1}{10}$ mm
(4) 1 mm
Show Answer
Answer: (1)
Solution
As we know,
Pressure amplitude, $\Delta P_0 = aKB = S_0 KB = S_0 \times \frac{\omega}{V} \times \rho V^2$
$\left[\because K = \frac{\omega}{V}, V = \sqrt{\frac{B}{\rho}}\right]$
$\Rightarrow S_0 = \frac{\Delta P_0}{\rho V\omega} = \frac{10}{1 \times 300 \times 1000}$ m $= \frac{1}{30}$ mm $= \frac{3}{100}$ mm
BETA
