Question

An aircraft is flying at an altitude where the ambient pressure is \(0.9\ \text{kPa}\) and the density is \(1226\ \text{kg/m}^3\). Calculate the velocity of sound when adiabatic index is \(1.226\).

• A. \(45\ \text{m/s}\)
• B. \(25\ \text{m/s}\)
• C. \(30\ \text{m/s}\)
• D. \(90\ \text{m/s}\)

Hint:

The speed of sound in a gas is \[ \boxed{ a=\sqrt{\frac{\gamma P}{\rho}}. } \] Higher pressure increases the speed of sound, while higher density decreases it.

Answer 1

The Correct Option is C

Step 1: Recall the velocity of sound formula. The velocity of sound in a gas is \[ \boxed{ a=\sqrt{\frac{\gamma P}{\rho}}, } \] where \[ \gamma \] is the adiabatic index.

Step 2: Substitute the given values. Given, \[ \gamma=1.226, \] \[ P=0.9\ \text{kPa}=900\ \text{Pa}, \] \[ \rho=1.226\ \text{kg/m}^3. \] Hence, \[ a = \sqrt{\frac{1.226\times900}{1.226}} = \sqrt{900} = 30\ \text{m/s}. \] Therefore, \[ \boxed{30\ \text{m/s}} \] is the correct answer. Thus, \[ \boxed{(C)} \] is the correct answer.