Question

A pressure of $10kPa$ causes a decrease is volume of water by $5\times {10}^{-3}$ percent. The speed of sound in water is

• A. $1414{ms}^{-1}$
• B. $1000m{s}^{-1}$
• C. $2000m{s}^{-1}$
• D. $3000{ms}^{-1}$

Answer 1

The correct option is A $1414{ms}^{-1}$

$B=\frac{dp}{\left(\frac{dv}{v}\right)}B=\frac{100\times {10}^3\times {10}^2}{5\times {10}^{-3}}=20\times {10}^8=2\times {10}^9\therefore v=\sqrt{\frac{B}{5}}=\sqrt{\frac{2\times {10}^4}{1000}}=\sqrt{2}\times {10}^3=1414m/s.$

Hence, the option $A$ is the correct answer.