Question

Pressure equation of a sound wave is $P=0.02\sin (3000t-9x)$ where all quantities are in $\text{SI}$ unit. The frequency and speed of sound wave is

• A. $\frac{1000}{\pi }\text{Hz},500\text{m/s}$
• B. $\frac{1500}{\pi }\text{Hz},\frac{1000}{3}\text{m/s}$
• C. $100\pi \text{Hz},250\text{m/s}$
• D. $200\pi \text{Hz},500\text{m/s}$

Answer 1

The correct option is B $\frac{1500}{\pi }\text{Hz},\frac{1000}{3}\text{m/s}$

On comparing, $P=0.02\sin (3000t-9x)$ with equation of travelling wave, $P=P_o\sin (\omega t-kx+\varphi )$
We get,
Angular frequency,
$\omega =3000\text{rad/s}$ and
wave number,
$k=9{\text{m}}^{-1}$
Now,
Speed of sound wave,
$v=\frac{\omega }{k}=\frac{3000}{9}=\frac{1000}{3}\text{m/s}$
Frequency,
$f=\frac{\omega }{2\pi }=\frac{3000}{2\pi }=\frac{1500}{\pi }\text{Hz}$