frequencies comparison
$begingroup$
I have a rather quiz question (sorry if this a wrong stack to ask such questions).
A propeller with 3 blades makes exactly 24 spins in 1 second. Camera, that is filming it, takes 54 frames in 1 second. How many photos that differ from one another were taken in 1 second?
I'm not sure how to approach this question. Comparing two frequencies and finding the point where they meet?
If I get the time for one propeller spin 1/24 and divide with time needed to take one picture it will result in ~ 2,23 pictures per propeller spin. But how do I find the point where camera starts taking same pictures?
contest-math
asked Nov 27 '18 at 10:22
BogdanBogdan
32
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add a comment |
$begingroup$
I have a rather quiz question (sorry if this a wrong stack to ask such questions).
A propeller with 3 blades makes exactly 24 spins in 1 second. Camera, that is filming it, takes 54 frames in 1 second. How many photos that differ from one another were taken in 1 second?
I'm not sure how to approach this question. Comparing two frequencies and finding the point where they meet?
If I get the time for one propeller spin 1/24 and divide with time needed to take one picture it will result in ~ 2,23 pictures per propeller spin. But how do I find the point where camera starts taking same pictures?
contest-math
asked Nov 27 '18 at 10:22
BogdanBogdan
32
$endgroup$
1
$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
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– José Carlos Santos
Nov 27 '18 at 10:26
add a comment |
$begingroup$
I have a rather quiz question (sorry if this a wrong stack to ask such questions).
A propeller with 3 blades makes exactly 24 spins in 1 second. Camera, that is filming it, takes 54 frames in 1 second. How many photos that differ from one another were taken in 1 second?
I'm not sure how to approach this question. Comparing two frequencies and finding the point where they meet?
If I get the time for one propeller spin 1/24 and divide with time needed to take one picture it will result in ~ 2,23 pictures per propeller spin. But how do I find the point where camera starts taking same pictures?
contest-math
asked Nov 27 '18 at 10:22
BogdanBogdan
32
$endgroup$
I have a rather quiz question (sorry if this a wrong stack to ask such questions).
A propeller with 3 blades makes exactly 24 spins in 1 second. Camera, that is filming it, takes 54 frames in 1 second. How many photos that differ from one another were taken in 1 second?
I'm not sure how to approach this question. Comparing two frequencies and finding the point where they meet?
If I get the time for one propeller spin 1/24 and divide with time needed to take one picture it will result in ~ 2,23 pictures per propeller spin. But how do I find the point where camera starts taking same pictures?
contest-math
contest-math
asked Nov 27 '18 at 10:22
BogdanBogdan
32
asked Nov 27 '18 at 10:22
BogdanBogdan
32
edited Nov 27 '18 at 10:30
Bogdan
asked Nov 27 '18 at 10:22
BogdanBogdan
32
asked Nov 27 '18 at 10:22
BogdanBogdan
32
asked Nov 27 '18 at 10:22
BogdanBogdan
32
32
1
$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Nov 27 '18 at 10:26
add a comment |
1
$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Nov 27 '18 at 10:26
1
1
$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Nov 27 '18 at 10:26
$begingroup$
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– José Carlos Santos
Nov 27 '18 at 10:26
add a comment |
1 Answer
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$begingroup$
You need to consider:
- the time it takes the propeller to move from its starting position to an identical-looking position; call this $t_p$ seconds.
- the interval between successive camera frames; call this $t_c$ seconds.
- the least common multiple of these two times: this is when the images start repeating. Call this $t_r$ seconds.
- the number of frames taken in either $t_r$ seconds or in 1 second, depending on which is shorter.
Assume the propeller blades are identical, so the propeller looks the same after $frac{1}{3}$ of a spin. 1 spin takes $frac{1}{24}$ of a second, so its appearance repeats in a third of that time. That is, $t_p=frac{1}{72}$.
From the problem description, we already know that the frame interval in seconds is $t_c=frac{1}{54}$.
Now we need the least common multiple of $t_r$ and $t_c$.
Noting that $54=3×18$ and $72=4×18$, we see that $3t_c = 4t_p = frac{1}{18}$. That is, in $frac{1}{18}$ of a second the camera takes 3 frames and the propeller position moves on by 4 identical-looking positions.
The answer is therefore 3 different images before they repeat.
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
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add a comment |
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$begingroup$
You need to consider:
- the time it takes the propeller to move from its starting position to an identical-looking position; call this $t_p$ seconds.
- the interval between successive camera frames; call this $t_c$ seconds.
- the least common multiple of these two times: this is when the images start repeating. Call this $t_r$ seconds.
- the number of frames taken in either $t_r$ seconds or in 1 second, depending on which is shorter.
Assume the propeller blades are identical, so the propeller looks the same after $frac{1}{3}$ of a spin. 1 spin takes $frac{1}{24}$ of a second, so its appearance repeats in a third of that time. That is, $t_p=frac{1}{72}$.
From the problem description, we already know that the frame interval in seconds is $t_c=frac{1}{54}$.
Now we need the least common multiple of $t_r$ and $t_c$.
Noting that $54=3×18$ and $72=4×18$, we see that $3t_c = 4t_p = frac{1}{18}$. That is, in $frac{1}{18}$ of a second the camera takes 3 frames and the propeller position moves on by 4 identical-looking positions.
The answer is therefore 3 different images before they repeat.
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
$endgroup$
add a comment |
$begingroup$
You need to consider:
- the time it takes the propeller to move from its starting position to an identical-looking position; call this $t_p$ seconds.
- the interval between successive camera frames; call this $t_c$ seconds.
- the least common multiple of these two times: this is when the images start repeating. Call this $t_r$ seconds.
- the number of frames taken in either $t_r$ seconds or in 1 second, depending on which is shorter.
Assume the propeller blades are identical, so the propeller looks the same after $frac{1}{3}$ of a spin. 1 spin takes $frac{1}{24}$ of a second, so its appearance repeats in a third of that time. That is, $t_p=frac{1}{72}$.
From the problem description, we already know that the frame interval in seconds is $t_c=frac{1}{54}$.
Now we need the least common multiple of $t_r$ and $t_c$.
Noting that $54=3×18$ and $72=4×18$, we see that $3t_c = 4t_p = frac{1}{18}$. That is, in $frac{1}{18}$ of a second the camera takes 3 frames and the propeller position moves on by 4 identical-looking positions.
The answer is therefore 3 different images before they repeat.
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
$endgroup$
add a comment |
$begingroup$
You need to consider:
- the time it takes the propeller to move from its starting position to an identical-looking position; call this $t_p$ seconds.
- the interval between successive camera frames; call this $t_c$ seconds.
- the least common multiple of these two times: this is when the images start repeating. Call this $t_r$ seconds.
- the number of frames taken in either $t_r$ seconds or in 1 second, depending on which is shorter.
Assume the propeller blades are identical, so the propeller looks the same after $frac{1}{3}$ of a spin. 1 spin takes $frac{1}{24}$ of a second, so its appearance repeats in a third of that time. That is, $t_p=frac{1}{72}$.
From the problem description, we already know that the frame interval in seconds is $t_c=frac{1}{54}$.
Now we need the least common multiple of $t_r$ and $t_c$.
Noting that $54=3×18$ and $72=4×18$, we see that $3t_c = 4t_p = frac{1}{18}$. That is, in $frac{1}{18}$ of a second the camera takes 3 frames and the propeller position moves on by 4 identical-looking positions.
The answer is therefore 3 different images before they repeat.
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
$endgroup$
You need to consider:
- the time it takes the propeller to move from its starting position to an identical-looking position; call this $t_p$ seconds.
- the interval between successive camera frames; call this $t_c$ seconds.
- the least common multiple of these two times: this is when the images start repeating. Call this $t_r$ seconds.
- the number of frames taken in either $t_r$ seconds or in 1 second, depending on which is shorter.
Assume the propeller blades are identical, so the propeller looks the same after $frac{1}{3}$ of a spin. 1 spin takes $frac{1}{24}$ of a second, so its appearance repeats in a third of that time. That is, $t_p=frac{1}{72}$.
From the problem description, we already know that the frame interval in seconds is $t_c=frac{1}{54}$.
Now we need the least common multiple of $t_r$ and $t_c$.
Noting that $54=3×18$ and $72=4×18$, we see that $3t_c = 4t_p = frac{1}{18}$. That is, in $frac{1}{18}$ of a second the camera takes 3 frames and the propeller position moves on by 4 identical-looking positions.
The answer is therefore 3 different images before they repeat.
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
edited Nov 27 '18 at 15:45
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
answered Nov 27 '18 at 15:39
timtfjtimtfj
1,706418
1,706418
add a comment |
add a comment |
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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
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– José Carlos Santos
Nov 27 '18 at 10:26