Doppler Effect of a 1-kilohertz sound

[Fanaticus]

Homework Statement

A source of 1-kilohertz sound is moving straight toward you at a speed .9 times the speed of sound. The frequency you receive is:

Homework Equations

$$\nu = \frac{v}{\lambda}$$

$$f' = \frac{v + v'}{v} f$$

The Attempt at a Solution

When I attempt the solution I get $$f' = \frac{v + .9v}{v} f = 1.9 f$$. However, that is not correct. The answer is 10 f. What am I missing?

Thx

 

[Dick]

Your sign on the relative velocity probably. You could also work on the algebra that let you change f'=1.9*f into f=1.9*f'. That doesn't seem right either.

 

[Fanaticus]

Well, the source is moving toward you. So the direction of the sound and the source should have the same sign. I don't know. I am missing something small I am sure, because this is a GRE question so it shouldn't take long to solve.

 

[Dick]

The formula I've got is f'=f*v/(v+vr). f' is observed frequency, f is emitted frequency. vr is radial component of source velocity. v is speed of sound. If it's moving towards you, you want an increase in frequency. That mean vr should be negative to make numerator larger than denominator.

 

[Fanaticus]

Ok, thx. The formula I was using seems to be for a moving listener not a moving source.

I see how you justify making the vr negative. However it still seems odd since vr and v are going in the same direction, know what I mean?

 

[Dick]

v is the speed of sound. It's isn't going in any particular direction. vr is coming towards you. Apparently according to the conventions of that formula that makes vr negative.