TPRH Science Workbook #366

[aspiringdoc09]

---

Members do not see this ad.

I know you all keep telling me to use the doppler approximation (I guess when possible) for Doppler effect questions, but it seems like TPRH wants us to complete the long calculations using the orignal Doppler effect equation. For instance:

#366. A stationary observer watching a train approach notices that, as the train passes by, the pitch of its whistle changes by one octave (that is, the perceived frequency decreases by a factor of 2) as the train recedes. If v is the speed of sound, what was the speed of train?

A. v/5
B. v/4
C. v/3
D. v/2

Is there a way to solve this problem using the doppler approximation? Hopefully, they are just testing concepts, because long drawn out calculations like this will take at least 2 minutes to setup if you remember the correct signs for each situation.

 

[pfaction]

I didn't even set this one up correctly, it seems. I did;

f1 = fs(V/V-Vs)
f2 = f1/2

I don't even understand why they did the 2nd part. My way does not work out though.

EDIT:

Oh wait, my way did work. Assuming I did the math right:
(V/V-VS)(1/2) = (V/V-S)
V/ (2V-2VS) = V/ (V-S)
Cross multiply them:
1 = 2V-2VS / V-VS
V-VS = 2V-2VS
-1V = -3VS
1/3V = VS
Wooo!

Not how you're supposed to do it but alternatives work. I don't know how you could have gotten this conceptually.

 

[aspiringdoc09]

I didn't even set this one up correctly, it seems. I did;

f1 = fs(V/V-Vs)
f2 = f1/2

I don't even understand why they did the 2nd part. My way does not work out though.

EDIT:

Oh wait, my way did work. Assuming I did the math right:
(V/V-VS)(1/2) = (V/V-S)
V/ (2V-2VS) = V/ (V-S)
Cross multiply them:
1 = 2V-2VS / V-VS
V-VS = 2V-2VS
-1V = -3VS
1/3V = VS
Wooo!

Not how you're supposed to do it but alternatives work. I don't know how you could have gotten this conceptually.

That's exactly what I was thinking. These questions should at least attempt to teach us to work them out conceptually. The math becomes bothersome. Also, they chose to use a + sign for one side but you still got the answer.

 

[pfaction]

The reason was they said the frequency decreased by two. When it's approaching, it's minus. Why bother doing the plus thing if it said that approaching frequency decreased by two when leaving? They used a plus and I had to divide a neg by a neg so I think it worked out in the end.