Calculating Doppler Effect: Car Speed and Frequency Analysis

[sonutulsiani]

Homework Statement

A car is approaching a reflecting wall. A stationary observer behind the car hears a sound of frequency 745 Hz from the car horn and a sound of frequency 863 Hz from the wall.

1. How fast is the car traveling?

A. 25.2 m/s
B. 33.4 m/s
C. 18.9 m/s
D. 54.2 m/s

2. The frequency of the car horn is

A. 690 Hz
B. 800 Hz
C. 804 Hz
D. 875 Hz

3. The frequency the car driver hears reflected from the wall is

A. 931 Hz
B. 804 Hz
C. 800 Hz
D. 926 Hz

I got 1 as 54.2 m/s but I am not sure about it. I don't know how to do the rest. Please help me out.

Homework Equations

The Attempt at a Solution

 

[ApexOfDE]

(1)
+ Observer - Carhorn: in this case, observer is fixed and source is moving => f = f0 * v / (v + vS)
+ Observer - wall: observer receives a sound hitting the wall from car => f = f0 * v / (v - vS)

(2) You have frequency in 2 situations, it will be easily to find f0.

(3) Car driver hears a sound reflected from the wall. The original frequency is the same that is incident upon the wall. In this case, you can consider driver as observer, the wall as source.

 

[sonutulsiani]

I didn't really understand what you just wrote..

1 is like we need to find the speed. What is f0, v and vs?
And why are there 2 equations, we just need one answer.

 

[ApexOfDE]

Sry for this unconvinience.

f is a frequency received by observer. v is, in this problem, speed of sound, and vS is speed of source.

(1)
+ observer - carhorn: because a car is driving away from observer and generates a sound, we can consider that car is source. Thus, eq for this is f1 = f0 * v / (v + vS), with f1 is sound frequency received by observer (745hz).

+ observer - wall: a wall reflects a sound from car. Original sound frequency is f0. But car is moving towards wall, therefore, wall will reflect a sound with frequency f2 instead of f0. f2 = f0 * v / (v - vS).

Because you don't have f0, you should combine these 2 eqs to find vS (in this case, vS is speed of car).

Hope this help.

 

[sonutulsiani]

Oh okay! I finally understood it, I got 1 as A - 25.2 m/s
2 as B - 800 HZ
And what will 3 be? 800 as well?

 

[ApexOfDE]

No. In last problem, car is not source but an observer. The source is a wall and you have a sound frequency reflected from a wall. Plug it into formula for moving observer case.

 

[sonutulsiani]

So it is 800*343/(343-25.2) = 863 ? But it's not there in the options.

 

[ApexOfDE]

No. You are using formula for moving source case. For moving observer, it should be f = f0 * (v +/- vO) / v (+ in the case observer is going towards source).

 

[sonutulsiani]

I got the 3rd 1 as 926. But then you said f0 is 863, what is f0? Isn't it the frequency of the car horn?

 

[sonutulsiani]

OH NO ! You have confused yourself : Here you have taken f2

Sry for this unconvinience.

f is a frequency received by observer. v is, in this problem, speed of sound, and vS is speed of source.

(1)
+ observer - carhorn: because a car is driving away from observer and generates a sound, we can consider that car is source. Thus, eq for this is f1 = f0 * v / (v + vS), with f1 is sound frequency received by observer (745hz).

+ observer - wall: a wall reflects a sound from car. Original sound frequency is f0. But car is moving towards wall, therefore, wall will reflect a sound with frequency f2 instead of f0. f2 = f0 * v / (v - vS).

Because you don't have f0, you should combine these 2 eqs to find vS (in this case, vS is speed of car).

Hope this help.

But here you have taken f2 as f0

No. You are using formula for moving source case. For moving observer, it should be f = f0 * (v +/- vO) / v (+ in the case observer is going towards source).

 

[ApexOfDE]

If car is not moving, f0 will be 800hz. However, car is going towards wall, so wall will receive a higher sound frequency and it will reflect this sound.

 

[sonutulsiani]

So the 2nd answer will be 804 Hz?

 

[ApexOfDE]

2B is right...

For 3rd problem, original f is 800hz, but source is moving, therefore, observer in wall will receive higher f. Wall receives this f and it reflect this f.

 

[sonutulsiani]

So that's what I get. 863 * (343+25.2)/343=926 Hz isn't it right?

 

[ApexOfDE]

D is correct. I never say you are wrong in 3rd :(

 

[sonutulsiani]

Ha ha, I said that long time back! Anyway, I understood it well! Thanks a lot for helping me :) Peace