Wavelength Physic Problems

Question

1)  When a police car is moving toward you, you hear its siren at 12.3kHz. When it is moving away from
you, you hear its siren at 10kHz. How fast is the police car moving, and what frequency is a police siren
at rest?

 

2) A plane flies directly over your head. When the plane is 32° above the horizon from your perspective,
you hear a sonic boom. How fast is the plane flying?

 

I need A little help, please.

Answer 1

(1)

 

I will set this up for you, but YOU do the calculations.  This is a Doppler shift problem.

 

v = speed of sound in air ≅ 345 m/s

v_s = speed of police car

f' = detected frequency

f = actual frequency

 

Moving toward you:

 

f' = f[v/(v - v_s)]

 

Equation (i):

 

12,300 = f[345/(345 - v_s)]

 

Moving away from you:

 

f' = f[v/(v + v_s)]

 

Equation (ii):

 

10,000 = f[345/(345 + v_s)]

 

With equations (i) and (ii), you have a system of 2 equations in the 2 unknowns f and v_s.  Solve the system for f and v_s.

 

(2)

 

This is a Mach cone problem.

 

v_s = speed of plane

v = speed of sound in air ≅ 345 m/s

 

Use the Mach cone relation

 

sinθ = v/v_s ⇒

 

v_s = v/sinθ = (345 m/s)/sin32° = ? m/s