Determine the number of N of digital bits

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Homework Help Overview

The discussion revolves around calculating the number of digital bits read by a CD player per second, based on the physical dimensions of the bits and the speed at which the CD spins. The subject area includes concepts from physics and mathematics, particularly relating to motion and measurement.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the conversion of units from meters to micrometers and discuss the relationship between speed and the number of bits read per second. Some draw analogies to a conveyor belt problem involving pencils to clarify their reasoning.

Discussion Status

There is an ongoing exploration of the calculations involved, with participants questioning the accuracy of their methods and the notation used for expressing large numbers. Some participants have provided guidance on unit conversions and the significance of notation in their school system.

Contextual Notes

Participants note that the term "digital bits" may be misleading and discuss the implications of using different numerical notations in their homework submissions. There is also mention of specific formatting requirements for answers in their educational context.

tavo0116
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On an audio compact disc (CD), digital bits of information are encoded sequentially along a spiral path. Each bit occupies about 0.28 um. A CD player's readout laser scans along the spiral's sequence of bits at a constant speed of about 1.2 m/s as the CD spins.

Determine the number N of digital bits that a CD player reads every second.

How should I start on this problem. Thank you !
 
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tavo0116 said:
On an audio compact disc (CD), digital bits of information are encoded sequentially along a spiral path. Each bit occupies about 0.28 um. A CD player's readout laser scans along the spiral's sequence of bits at a constant speed of about 1.2 m/s as the CD spins.

Determine the number N of digital bits that a CD player reads every second.

How should I start on this problem. Thank you !

If you had a conveyor belt going past at 5 m/s, and it was loaded with pencils arranged sideways on the belt, touching each other, and each pencil is 4mm in diameter - how many pencils pass each second.

You CD is like that with different sizes involved.
 
Just FYI, the phrase "digital bits" is a nonsensical. "Bits" means BINARY digits, not decimal digits.
 
PeterO said:
If you had a conveyor belt going past at 5 m/s, and it was loaded with pencils arranged sideways on the belt, touching each other, and each pencil is 4mm in diameter - how many pencils pass each second.

You CD is like that with different sizes involved.

So I would need to convert 5m/s to mm, which will then give me 5000mm/s?
Then in order to fill the number of pencils pass each second, I would take 5000 mm/4 mm, which will then give me 1250 pencils?

As for the problem I posted, um is micrometer, right?
So then I would need to convert 1.2 m/s to 1200000 um/s?

Then as I did before, I would need to take 1200000 um / 0.28 um, which will then give me 42.86E^6?
 
tavo0116 said:
So I would need to convert 5m/s to mm, which will then give me 5000mm/s?
Then in order to fill the number of pencils pass each second, I would take 5000 mm/4 mm, which will then give me 1250 pencils?

As for the problem I posted, um is micrometer, right?
So then I would need to convert 1.2 m/s to 1200000 um/s?

Then as I did before, I would need to take 1200000 um / 0.28 um, which will then give me 42.86E^6?

That should be correct [I didn't check the calculation]. though that answer would be marked wrong in our school system. You have merely written down what the calculator said.

You should have said 4.3 x 10^7 [assuming you answer was correct] [or 43 x 10^6 if you are using engineering notation]

As I said, any submitted answer here, with an E in it, marked WRONG.

[and why only 4.3 rather than 4.286?]
 
PeterO said:
That should be correct [I didn't check the calculation]. though that answer would be marked wrong in our school system. You have merely written down what the calculator said.

You should have said 4.3 x 10^7 [assuming you answer was correct] [or 43 x 10^6 if you are using engineering notation]

As I said, any submitted answer here, with an E in it, marked WRONG.

[and why only 4.3 rather than 4.286?]

I calculated that, and entered it in the system as 4.3 x 10^7, and it was right.
This was for an online homework problem.

Thank you so much for your help.
Have a great day !
 

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