Travelling towards a Canyon Wall: Calculating Beat Frequency

[John Ker]

Homework Statement

1. On a long trip that you take to forget for a while about physics, you find yourself driving
directly towards a canyon wall. You’ve previously noticed that your car horn has a
frequency of 440 Hz. You glance at the speedometer and notice you’re moving at 30
km/h. (8.333...m/s)
What is the beat frequency you experience?

Homework Equations

Various Doppler Effect Equations and Beat Frequency

The Attempt at a Solution

I need to calculate the beat frequency for this question, to do that I need both frequencies from the reflection of the wall and the sound I hear from the horn itself.
Is it correct to treat the wall as its own source? Therefore I am traveling towards the source?
What about the second doppler effect? I am struggling to figure it out. It is me traveling towards the source again? That wouldn't make sense as I am traveling to two sources? ahh I am stuck.
(How does the frequency change when I am traveling with the source?)

Thanks!

 

[kuruman]

Imagine an observer standing right next to the wall towards whom you are moving. What frequency does this observer hear? That's the frequency that is reflected off the wall which you may take as a source. Now you are moving towards that secondary wall source. What frequency do you hear coming from the wall? That frequency is beating against the frequency of the source that you are carrying with you (440 Hz).

 

[John Ker]

Imagine an observer standing right next to the wall towards whom you are moving. What frequency does this observer hear? That's the frequency that is reflected off the wall which you may take as a source. Now you are moving towards that secondary wall source. What frequency do you hear coming from the wall? That frequency is beating against the frequency of the source that you are carrying with you (440 Hz).

Ohh, so the hint in the question is not referring to 2 separate doppler effects, rather 2 doppler effects on the same wave that beats with the initial source.

Sooo...
EQN 1: Source moving towards observer: f_1 = 440 [ 1 / (1 - 8.33... / 340) = 429.47 Hz
EQN 2: Observer moving towards source: f_2 = 429... [ 1 + 8.33../340]
This gives 462.11
Beat Frequency =

462.11 - 440 ~ 22 Hz (Which is correct answer)

Thank you!

Ps. For any source that I am traveling with, let's say I am on a swing with a whistle that is 400 Hz, I will experience 400 Hz because both me and the whistle are traveling together?

 

[kuruman]

Ps. For any source that I am traveling with, let's say I am on a swing with a whistle that is 400 Hz, I will experience 400 Hz because both me and the whistle are traveling together?

Yes. You are at rest with respect to the source so you hear the unshifted frequency.