Question

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)

• A. 0.3 m
• B. 0.4 m
• C. 0.36 m
• D. None of these

Answer 1

The correct option is C

0.36 m

Given $f=1000Hz$, $A_0=1.2\times {10}^{-8}$m

$\Delta P_0=3\times {10}^{-2}Pa$

WE known $\Delta P_0=B{A}_{0}K$

$\Rightarrow \Delta P_0=B.A_0.\left(\frac{2\pi }{\lambda }\right)$

$\lambda =\frac{B.A_{0}2\pi }{\Delta P}$

$=\frac{1.42\times {10}^5\times 1.2\times {10}^{-8}\times 2\pi }{3\times {10}^{-2}}$

=0.36m