# Question concerning Doppler effect

Tags:
1. Oct 14, 2015

### diredragon

1. The problem statement, all variables and given/known data
In the picture below, can you help me understand what do equations 3 and 5 mean. They concern the soppler effect but i cant seem to understand what do they represent.

2. Relevant equations
ft + fv/c=ft((c+v)/c
fd=ft-fr

3. The attempt at solution

#### Attached Files:

• ###### 20151014_204937.jpg
File size:
39.4 KB
Views:
63
2. Oct 14, 2015

### haruspex

I find it impossible to read the subscripts in the posted image. Too blurred. Please try again, maybe just extracting the relevant part instead of the whole page.

3. Oct 14, 2015

### diredragon

4. Oct 15, 2015

### haruspex

That helps.
The first equation in section 62 has a typo. The fr on the right should be ft.
The third equation is even worse. The fv/c should read ftv/c.

Not sure what your difficulty is with the fifth equation. The 'x' in the middle is supposed to be multiplication. The set-up for this equation is somewhat special: it describes it as the receiver receiving the waves only after reflection off a surface, and both transmitter and receiver happening to be travelling at the same speed v towards that surface. Is that interesting?
More useful would be a general equation with source and receiver each moving, at different speeds, relative to the medium.

One thing to note in all this is that speeds relative to medium is important. As a result, the source moving towards a stationary receiver (relative to the medium) at speed v gives a different effect from the receiver moving towards a medium-stationary source at speed v. In an extreme case, if the source moves towards the receiver at the speed of sound then the frequency becomes infinite, whereas if the receiver moves towards the source at that speed the frquency merely doubles.

5. Oct 15, 2015

### diredragon

I didnt understand what does the third equation describe its frequency minus 1/distance and the fifth multiplaying the frequancy with thw expression c-a/v what does that mean? Has something to do woth reflecting surfaces i suppose. Its full of typos

6. Oct 15, 2015

### haruspex

Are we on page 62? I don't see anything about frequency minus 1/distance, or c-a/v. Please type out the whole equations that you are referring to.

Last edited: Oct 15, 2015
7. Oct 15, 2015

### diredragon

Yes still on 62, it says 1/u=f/v
Where u is wavelenght and the next equation says ft + f/c does that make it so?

8. Oct 15, 2015

### haruspex

No, it doesn't say 1/lambda = f/v, it says 1/lambda=f/c.
For the next equation, as I explained in post #4, that fv/c is wrong. It should say ftv/c.

9. Oct 15, 2015

### diredragon

From your post number 4 you say the it is important which moves towarda which but isnt that ignorable in special relativity where motion becomes relative?

10. Oct 15, 2015

### haruspex

In relative motions of bodies and light, there is no medium to worry about. Here there is.
If a plane flies towards you at the speed of sound, the wavefronts stack up on the front of the plane. When it reaches you, you hear them all at once, an infinite frequency.
If you move towards a sound source at the speed of sound, your rate of encountring wavefronts doubles, doubling the frequency.

11. Oct 16, 2015

### diredragon

Whoch frequencies are emitted from this device? Do you know? It says radio waves but i keep hearing from my teacher they are ultrasonic. What do you think?

12. Oct 16, 2015

### haruspex

Which device?
The discussion on page 62 starts by mentioning a sound source, but there are no numbers given, so it could be any frequencies.

At the bottom of the page it then adapts the equation to electromagnetic radiation. However, I note something of a blunder there. It simplifies the equation on the basis that the velocities of the objects are small compared to the speed of light. The equation would be different anyway: light does not travel through a medium, so the equations developed for sound propagation would be wrong. The low-speed simplification comes out the same for both, though.

On page 63 it discusses sonar, so we are back to sound waves.

13. Oct 16, 2015

### diredragon

It is a description of doppler speed logn device used on ships to calculate the speed at which they move. It emits two rays towards the sea bottom, one upfront and one behind so im wondering whoch waves that are

14. Oct 16, 2015

### haruspex

Ok, so it's the device discussed on page 63 and following. It uses sonar, so we're discussing sound waves, not radio waves.
(Where are you reading radio waves? There's a different device discussed earlier which uses electromagnetic induction to measure speed.)

On page 69 I finally found a mention of frequency range, 100kHz to 1MHz. That puts it well into ultrasonic, which is any sound wave over 20kHz.

This is an interesting document, but contains an alarming number of errors. The discussion on page 65 of how the Janus system compensates for trim is mathematically nonsense.

15. Oct 17, 2015

### diredragon

It discusses radio waves on page 60 - 62. Doppler speed log its called and i think the next chapters are all nonsense, but it describes the working of the device from 60 - 63. The document contains many ways to measure speed and page 62 is the middle of the description of the doppler speed log. It starts genereal discussion on it earlier.

16. Oct 17, 2015

### haruspex

I think you are confusing two devices.
In your post #13 you described the ship emitting waves down into the water, fore and aft. Those have to be sound waves. Electromagnetic (i.e. radio) waves are notoriously poor at going through water.

It's structured like this:
Section 3.3 describes a device using electromagnetic induction. Any radio waves involved are not required to penetrate far into the water.
Section 3.4 describes a device using sound waves (sonar). Didn't try to follow the details, but it does involve echoes from the seabed.
Section 3.5 discusses the Doppler effect in general terms. The Doppler effect arises both in sound waves and radio waves.
Section 3.6 goes on to describe a device using sound waves and the Doppler effect. This one has the fore-and-aft emitters.

So, those four sections between them cover three different devices. Which one is of interest to you?

17. Oct 17, 2015

### diredragon

The one using the fore and aft beam transmission and echo of the seabed to calculate the speed using doppler principle. So i guess it uses then the sound waves? Could they be ultrasonic?

18. Oct 17, 2015

### haruspex

As I wrote in post #14, it seems they are ultrasonic.