Question

Calculate the bulk modulus of the air from the following data about a sound wave of wavelength $35cm$ travelling in air. the pressure at a point varies between $\left(1.0\times {10}^5\pm 14\right)Pa$ and the particles of the air vibrate in simple harmonic motion of amplitudes $5.5\times {10}^{-6}m$.

• A. $3.2\times {10}^{2}N{m}^2$
• B. $5.5\times {10}^{6}N{m}^2$
• C. $1.4\times {10}^{5}N{m}^2$
• D. None of these

Answer 1

The correct option is C

$1.4\times {10}^{5}N{m}^2$

Step 1. Given data

Wavelength of the sound wave, $\lambda =35cm$

Pressure amplitude, $p_0=\left(1\times {10}^5\pm 14\right)pa$ [It is the pressure that varies]

Displacement amplitude, $S_0=5.5\times {10}^{-6}m$

Step 2. Finding the Bulk modulus, $B$

By using the formula of the Bulk modulus,

$B=\frac{p_0\lambda }{2{\mathrm{\pi S}}_0}$

$B=\frac{14\times 35\times {10}^{-2}}{2\times 3.14\times 5.5\times {10}^{-6}}$ [$1cm={10}^{-2}m$]

$B=1.4\times {10}^{5}N{m}^2$

Hence, the correct option is $\left(C\right)$.