frequency flashlight

[chiddler]

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A car travels at night at 10 m/s past a row of identical trees. Each tree is 1 m thick and is 1 m away from other trees. A child watching the trees go by flickers a flashlight at 4 times per second. If a child can only see trees when the flash light is on, how fast will the trees appear to pass by?

1, 4, 9, or 20?

Answer is 1.

Their explanation: Five trees pass each second. This is a frequency of 5. The frequency of the flashing light and the frequency of the passing trees creates a beat frequency of 5-4 = 1.

Looking for a better explanation than EK's "its beat frequency", please.

 

[MedPR]

"How fast will the trees appear to pass by?" Is the answer in m/s? Trees per second?


Oh, nevermind I see what you meant. Thinking...

The beat frequency is the only equation I can think to use, but here's another way to think about it.

The girl can potentially see a tree 4 times per second since her light is on 4 times per second. While moving at 10m/s, she will be passing a tree every, as you say, every 0.2 seconds. So say her flashlight is on at 0 seconds, and we are in front of a tree at 0 seconds.

She sees a tree at 0 seconds.

At 0.2 seconds we are in front of the next tree, but her flash light is off. It goes on again at 0.25 seconds, when we are in a space.

The next tree is at 0.4 seconds. Her flashlight is off again, and doesn't go on until 0.5 seconds, where we are in a space.

The next tree is 0.6 seconds. Her flashlight is off again, and doesn't go on until 0.75 seconds, where we are in a space.

The next tree is 0.8 seconds. Her flashlight is off again, and doesn't go on until 1 second, where we will be at another tree.

The next tree is at 1 second, her light is on, and she sees this tree.

This is what I came up with, but it is inconsistent with the answer.

 

[milski]

Whoever wrote the question has no idea what a beat frequency is. You need the two signals that you're talking about to be able to interfere and you need them both to be simple harmonics. The situation described below is neither so trying to twist into beat frequencies is inadequate to say the least. Your approach is perfectly reasonable.

 

[MedPR]

Maybe I'm the only one, but knowing the units of the answer would make this easier for me to think about.

 

[chiddler]

it's trees per second. i erased my approach because i realized that the 0.2 seconds includes both tree and gap. so it's not necessarily a tree in that 0.2 seconds, but can be gap as well.

however, you did it more correctly because you you didn't look at it in 0.2 second blocks as I did. rather, the discrete moment at 0, 0.2, 0.4 is the moment where the trees are visible and for 0.1 seconds after that.

thanks for the help.

 

[milski]

Here is an attempt for an illustration. The yellow dashed line on the top represents a tree present next to the car - 5 trees per second, 5 gaps per second - total of 10 m. The pink line represents the flashlight being on - 4 times per second. The girl sees a tree only when there is both yellow and pink - these are the areas represented as blue dashes below.

I don't see how this can interpreted as 1 tree per second. 😕

 

[chiddler]

interesting graph. they must mean when you see the entire 1 m of the tree...

 

[milski]

interesting graph. they must mean when you see the entire 1 m of the tree...

Yes, that will probably end up being as 1 Hz. Frequency as an answer to how fast the trees pass by is sort of messed up, especially considering that at some points she'll see the ends of the trees. I still don't like the question and think that they're trying to apply a concept in a situation where it is not applicable.

 

[MedPR]

Well if she sees a tree at 0 seconds, 1 second, 2 seconds, 3 seconds, etc (this is what I got from my method above), then I guess she does see only 1 tree per second?

I'm not really understanding how the beat frequency works though.

 

[milski]

But she sees a bit of tree at other intervals as well - from 0.25 s to 0.3 s for example. Does seeing a tree slide in or out of view count? And what exactly is "how fast the trees appear to pass by"?

On the beat frequencies: There is an earlier post with some graphs there but the major idea is that you have two interfering harmonic waves with similar frequencies. The waves have to be able to interfere with each other - you're not going to get any beat frequency sending a sound wave over a water surface vibrating with similar frequency. They also have to be simple harmonics - that allows you to write a simple formula for each of them and to simplify combination of the two waves a product of two cosines. The result is a wave with a frequency/pitch the average of the two initial waves and continuously changing amplitude. The frequency of amplitude change is what is called 'beat frequency'. If you are adding non-harmonic waves, all bets are off about what you're going to get as a result - it can be much more complicated and can be any sort of wave.

 

[MedPR]

But she sees a bit of tree at other intervals as well - from 0.25 s to 0.3 s for example. Does seeing a tree slide in or out of view count? And what exactly is "how fast the trees appear to pass by"?

On the beat frequencies: There is an earlier post with some graphs there but the major idea is that you have two interfering harmonic waves with similar frequencies. The waves have to be able to interfere with each other - you're not going to get any beat frequency sending a sound wave over a water surface vibrating with similar frequency. They also have to be simple harmonics - that allows you to write a simple formula for each of them and to simplify combination of the two waves a product of two cosines. The result is a wave with a frequency/pitch the average of the two initial waves and continuously changing amplitude. The frequency of amplitude change is what is called 'beat frequency'. If you are adding non-harmonic waves, all bets are off about what you're going to get as a result - it can be much more complicated and can be any sort of wave.

At 0.3 seconds her light is off, so she sees nothing. If she is at the middle of a tree at 0.2 seconds, at 0.25 seconds she has already passed the tree and is right at the start of the space.

Right? Maybe I'm missing something too 🙁

 

[milski]

At 0.3 seconds her light is off, so she sees nothing. If she is at the middle of a tree at 0.2 seconds, at 0.25 seconds she has already passed the tree and is right at the start of the space.

Right? Maybe I'm missing something too 🙁

The light is on from 0.25 to 0.375. There is a tree next to her from 0.2 to 0.3. So she should be seeing tree from 0.25 to 0.3 and no tree from 0.3 to 0.375. So she should see a tree disappear during that period of light.

 

[MedPR]

The light is on from 0.25 to 0.375. There is a tree next to her from 0.2 to 0.3. So she should be seeing tree from 0.25 to 0.3 and no tree from 0.3 to 0.375. So she should see a tree disappear during that period of light.

Where did we get the info that the light is on for more than an instant? I thought we were assuming the light went on at 0.25 and off at 0.25.

 

[milski]

Where did we get the info that the light is on for more than an instant? I thought we were assuming the light went on at 0.25 and off at 0.25.

There is no info either way - all they say is that the light is flickered on 4 times a second. Saying that it's instantaneous might be a way to make their answer work.

 

[MedPR]

There is no info either way - all they say is that the light is flickered on 4 times a second. Saying that it's instantaneous might be a way to make their answer work.

I just assumed it was instantaneous, otherwise we would never be able to get an answer because even if the amount of time we left the light on was constant, the number of whole or partial trees that she sees would be different depending on what interval of time we are talking about. Meaning, if she saw X number of trees in 10 seconds, she wouldn't see 5x in 50 seconds.