Chapter 2: Q57E (page 541)

A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle $σ$ of the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.

Short Answer

Expert verified

a) Angle of the shock-wave cone is $α = 36 . 03^{c}$

b) Time taken is $2.94 s$

Step by step solution

Step 1:

Given data:

The shock wave is produced by a sound source that moves faster than sound

$\sin α = \frac{v}{v_{S}}$

Here,

$v \to$ speed of sound

$v_{s} \to$ speed of source

localid="1664344351725" $α \to$ angle of shock wave

Step 2:

a) As the Mach number $= \frac{v_{S}}{v} = 1.7$

$\begin{array}{l} sim = \frac{v}{v_{S}} = \frac{1}{1.7} \\ α = s i n^{- 1} (\frac{1}{1.7}) = 36 . 03^{o} \end{array}$

Hence, the angle of the shock-wave cone is $α = 36 . 03^{°}$

Step 3:

b) Time-taken is

$Tanα = \tan 36 . 03^{°} = \frac{d}{v_{S^{}} t} = 0.727$

On putting the values;

$t = \frac{d}{v_{s} \times 0.727} = \frac{1250 m}{0.727 \times 1.7 \times 344 m / s} = 2.94 s$

Hence, the time taken is $2.94 s$

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A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle $σ$ of the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.

Short Answer

Step by step solution

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Step 2:

Step 3:

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A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle σof the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.

Short Answer

Step by step solution

Step 1:

Step 2:

Step 3:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Fluids

Atoms and Radioactivity

Astrophysics

Physical Quantities And Units

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle $σ$ of the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.