# Travelling towards a Canyon Wall: Calculating Beat Frequency

• John Ker
In summary, the beat frequency experienced when traveling towards a wall with a car horn frequency of 440 Hz and a speed of 30 km/h is 22 Hz, calculated using two Doppler effect equations. The wall is treated as a secondary source and the observer hears a frequency of 462.11 Hz, causing a beat frequency of 22 Hz when combined with the 440 Hz frequency of the car horn. Additionally, when traveling with a source, the observer will hear the unshifted 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!

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).

kuruman said:
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?

John Ker said:
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.

John Ker

## 1. What is the purpose of calculating beat frequency while travelling towards a canyon wall?

The purpose of calculating beat frequency while travelling towards a canyon wall is to measure the change in frequency of sound waves as they approach a stationary object. This can provide valuable information about the speed and direction of the moving object, as well as the distance between the object and the stationary wall.

## 2. How is beat frequency calculated in this scenario?

In this scenario, beat frequency is calculated by taking the difference between the frequency of the sound waves emitted by the moving object and the frequency of the reflected sound waves bouncing off the stationary canyon wall. This difference in frequency is known as the beat frequency.

## 3. What factors can affect the accuracy of calculating beat frequency?

The accuracy of calculating beat frequency can be affected by several factors, including the speed of the moving object, the distance between the object and the canyon wall, and any obstructions or obstacles that may interfere with the sound waves. Additionally, environmental factors such as wind or temperature can also impact the accuracy of the calculations.

## 4. What can be learned from analyzing beat frequency while travelling towards a canyon wall?

By analyzing beat frequency while travelling towards a canyon wall, valuable information can be gained about the speed and direction of the moving object, as well as the distance between the object and the stationary wall. This data can also be used to study the acoustics of the canyon and how sound waves behave in this particular environment.

## 5. Are there any real-world applications for calculating beat frequency in this scenario?

Yes, there are several real-world applications for calculating beat frequency while travelling towards a canyon wall. For example, this method can be used by scientists to study the movements of animals in their natural habitat, as well as by engineers to design and test sonar and radar systems. It can also be applied in fields such as geology and seismology to study the properties of different types of terrain.

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