TBR: Doppler Effect Equation

[justadream]

TBR Physics Book II page 26 #20

"Starting with Surmarine USA [the SOURCE] on the left and the Submarine CIS [the DETECTOR] on the right, which condition will lead to the lowest observed frequency for Submarine CIS"

Btw: Source frequency is 500hz. Sound wave is 1500 m/s.

Answer: Submarine USA moving to the left at 10 m/s, with Submarine CIS moving to the right at 10 m/s

I get this.

But I'm confused about how TBR shows the calculation for situation in the answer explanation as:

f = 500 (1500 + 10) / (1500 - 20)

Why is there a 20? The bottom should be the relative movement of the source. Shouldn't that be 10?

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[type12]

The relative movement is the difference between their velocities. The easiest way to simplify this for the MCAT is to rethink the problem, making either the observer (detector) or source stationary.

Remember, velocity also has direction, so if it's -10 m/s for the USA, and CIS +10 m/s, the difference in their velocities is -20 m/s (-10 - +10). Now, if we made CIS stationary, USA is moving to the left at 20 m/s; if we made USA stationary, CIS is moving 20 m/s to the right.

 

[justadream]

@type12

Using this logic, then why do you only have 10 in the numerator (not 20)

Another problem I have is that there is a difference whether the detector or the source moves.

(1500 + 10) / 1500 is different from 1500 / (1500-10)

 

[type12]

That's relative to the medium. The actual form of the doppler equation can be confusing, so, since you're not necessarily interested in physics, it's easier to see if you use the MCAT-recommended version of the equation:

change in f / original f = delta v (this is difference in velocities) / c (speed of waves in medium)

 

[justadream]

@type12

Yes, I know about that formula (from EK). Are there limitations to when it can be used?

With regard to the original equation, are you saying that you should only care about relative velocity in the denominator (which accounts for source).