Question

If the critical speed of sound is \(300\ \text{m/s}\), upstream velocity across the normal shock wave is \(600\ \text{m/s}\), the downstream velocity is

• A. \(175\ \text{m/s}\)
• B. \(150\ \text{m/s}\)
• C. \(225\ \text{m/s}\)
• D. \(178\ \text{m/s}\)

Hint:

Across a normal shock, \[ \boxed{ V_1V_2=a^{*2} } \] where \[ a^* \] is the critical speed of sound.

Answer 1

The Correct Option is B

Step 1: Use the normal shock relation. For a normal shock, \[ \boxed{ V_1V_2=a^{*2}, } \] where \[ a^* \] is the critical speed of sound.

Step 2: Substitute the given values. Given, \[ a^*=300\ \text{m/s}, \] \[ V_1=600\ \text{m/s}. \] Hence, \[ V_2 = \frac{a^{*2}}{V_1} = \frac{300^2}{600}. \] \[ = \frac{90000}{600} = 150\ \text{m/s}. \] Therefore, \[ \boxed{150\ \text{m/s}} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.