Doppler Effect? Happy Thanksgiving

[valeriex0x]

Homework Statement

The frequency ratio of a semitone interval on the equally tempered scale is 2 1/12.
A) Show that the ratio is 1.059
B) Find the speed of an automobile passing a listener in still air if the pitch of the car's horn drops a semitone between the times when the car is coming directly toward him and when it is moving directly away from him.

Homework Equations

twords fL= v/λ + vL/λ

away fL= v/λ - vL/λ

The Attempt at a Solution

I'm not sure how to start part A, and i need that info for part b. please advise!

 

[cepheid]

Homework Statement

The frequency ratio of a semitone interval on the equally tempered scale is 2 1/12.
A) Show that the ratio is 1.059

The ratio of what? The only ratio that is mentioned in the problem is the frequency ratio of a semitone, which is already given as 2\tfrac{1}{12}. So I'm a little puzzled as to what this part is asking for.

B) Find the speed of an automobile passing a listener in still air if the pitch of the car's horn drops a semitone between the times when the car is coming directly toward him and when it is moving directly away from him.

Homework Equations

twords fL= v/λ + vL/λ

away fL= v/λ - vL/λ

The Attempt at a Solution

I'm not sure how to start part A, and i need that info for part b. please advise!

If you have an equation for the Doppler effect in the form of f = f₀*(blah) where f is the observed frequency and f₀ is the original (emitted) frequency, then solving this part shouldn't be too difficult.

 

[valeriex0x]

The title of the question is "Musical Scale."

Part A seems so confusing to me. That is all they gave in the question.

:/

 

[valeriex0x]

They don't give me any numbers for part B.

 

[cepheid]

The title of the question is "Musical Scale."

Part A seems so confusing to me. That is all they gave in the question.

:/

AH I see. It's not 2\tfrac{1}{12}. It is 2^{\frac{1}{12}}. Check this out:

http://en.wikipedia.org/wiki/Equal_temperament
http://en.wikipedia.org/wiki/Twelfth_root_of_two

That makes part (a) exceptionally simple.

 

[valeriex0x]

hmmmm okay. thanks for those links. So do you think they just want me to type in 12 rad 2 for part A. I kind of don't get it.

I saw for b, that the distances are equally apart.

 

[valeriex0x]

yayy! I typed in 12 rad 2 and i got it right!

 

[valeriex0x]

Could you explain How i should set up part b.

 

[valeriex0x]

The only thing I can think of this that from A, if they are saying that the frequency ratio is 2^(1/12), then If I want to find the Period, T=1/f or T= 1/ 2^(1/12) = 0.9438
?

 

[valeriex0x]

Frequency of the Listener = ( (v+vL)/(v+vs) )* Frequency of source 2^ 1/12:( I'm not sure I'm understanding how to find my other variables.

 

[cepheid]

hmmmm okay. thanks for those links. So do you think they just want me to type in 12 rad 2 for part A. I kind of don't get it.

The twelfth root of 2 is approximately 1.059. Unless if you have logarithm tables or something, I really don't know how you are expected to "show" this, aside from plugging it into your calculator. You could show that (1.059)¹² ≈ 2, but again, this involves merely plugging it into your calculator. So it seems like somewhat of a useless question.

There is almost certainly some fancy way of computing it by hand without a calculator, but I somehow doubt your physics teacher wants you to delve into that.

I saw for b, that the distances are equally apart.

Again, like I said before, if you've covered the Doppler effect in class, then you undoubtedly
derived an equation that shows how the observed frequency depends on the emitted frequency and on the relative velocity between the source and the observer. All you have to do is use this equation for both the "towards" and "away" cases.

 

[cepheid]

Frequency of the Listener = ( (v+vL)/(v+vs) )* Frequency of source 2^ 1/12


:( I'm not sure I'm understanding how to find my other variables.

That's closer, but it's not quite what they're saying in the problem. In the problem, they're saying that:

[frequency of listener (towards)] / [frequency of listener (away)] = 2^1/12

So you get to plug in the Doppler formula for both the numerator and for the denominator of this fraction. Only the the velocity of the source changes between the two cases. You can take the velocity of the listener to be 0.

 

[valeriex0x]

No, He ended class with interference. So I am just trying to figure this out by watching videos online and stuff. I tried doing the next two problems and I got them wrong (see the pic for the work) So that is why i am confused!

 

[valeriex0x]

That's closer, but it's not quite what they're saying in the problem. In the problem, they're saying that:

[frequency of listener (towards)] / [frequency of listener (away)] = 2^1/12

So you get to plug in the Doppler formula for both the numerator and for the denominator of this fraction. Only the the velocity of the source changes between the two cases. You can take the velocity of the listener to be 0.

When I plug in vListener/λ that goes to zero in both the numerator and the denominator. I am just left with

(v/λ)/(v/λ)=2^1/12

will the v divided by lamdas equal 1. 1 is not equal to 2 1/12?

 

[cepheid]

No, He ended class with interference. So I am just trying to figure this out by watching videos online and stuff. I tried doing the next two problems and I got them wrong (see the pic for the work) So that is why i am confused!

Okay, so you haven't done the Doppler effect in class yet (do you not have a textbook though?). In any case, it sounds like you found the right equation just through searching online. It's also explained really clearly here:

http://en.wikipedia.org/wiki/Doppler_effect#General

When I plug in vListener/λ that goes to zero in both the numerator and the denominator. I am just left with

(v/λ)/(v/λ)=2^1/12

will the v divided by lamdas equal 1. 1 is not equal to 2 1/12?

Huh? No. Use the equation you posted in post #10 (without the 2^12 factor). I responded in post #12 saying that that was the correct equation, but that you'd have to apply it twice, once in the numerator and once in the denominator of your ratio. You'll see that the frequency of the source will cancel from top and bottom.

 

[brianyun]

Heh, I assume you are from QC with Dr. Steiner.

The numerator and denominator aren't exactly the same.

In numerator, it's (V+VL)/(V-VS) while the denominator is (V+VL)/(V+VS). The frequency of the source is canceled out.

You know that VL is 0. You know that [(V+VL)/(V-VS)]/[(V+VL)/(V+VS)] = 2^(1/12). You know V = 344 m/s. Solve for VS!