Question about math of unknown discipline

[tycallsky]

I'm sorry, but I do not know what discipline of math this problem would fall under. Here is my question:

lets say you have a repeated noise every 1 second. You have another noise repeating every 1 and 1/2 seconds, another every 1 and 1/4 seconds and so on. When will these beats intersect perfectly? Here are all the variables:
x
x+1/2
x+1/4
x+1/8
x+1/16
x+1/32
x+1/64
x+1/128

when will those all intersect? I think it might require trig or calc, but I'm not sure. I've only taken College Algebra. Maybe you guys can help! A good way to imagine this is if you have a ship in space orbiting an object every x interval, another ship orbiting at x+1/2 etc. When will all 8 ships be aligned.

Thanks for the help!

Tyler

 

[stapel]

lets say you have a repeated noise every 1 second. You have another noise repeating every 1 and 1/2 seconds, another every 1 and 1/4 seconds and so on. When will these beats intersect perfectly? Here are all the variables:
x
x+1/2
x+1/4
x+1/8
x+1/16
x+1/32
x+1/64
x+1/128

when will those all intersect? I think it might require trig or calc, but I'm not sure....

For what does "x" stand? How did you plan to use trigonometry or calculus? (This looks like a pre-algebra least-common-multiple exercise, is why I ask.)

Please be complete. Thank you!

 

[Ishuda]

I'm sorry, but I do not know what discipline of math this problem would fall under. Here is my question:

lets say you have a repeated noise every 1 second. You have another noise repeating every 1 and 1/2 seconds, another every 1 and 1/4 seconds and so on. When will these beats intersect perfectly? Here are all the variables:
x
x+1/2
x+1/4
x+1/8
x+1/16
x+1/32
x+1/64
x+1/128

when will those all intersect? I think it might require trig or calc, but I'm not sure. I've only taken College Algebra. Maybe you guys can help! A good way to imagine this is if you have a ship in space orbiting an object every x interval, another ship orbiting at x+1/2 etc. When will all 8 ships be aligned.

Thanks for the help!

Tyler

Bell 0 [the x bell] goes off every second. Bell 1 [the x+1/2=x+1/2¹ bell] goes off on the second every two seconds, so at seconds 1+ 2ⁿ, bell 0 and bell 1 ring at the same time. Bell 2 [the x+1/4=x+1/2² bell] goes off on the second every 4 seconds so bell 0 and bell two go off together at every 1+ 4ⁿ seconds. However, since 1 + 4ⁿ = 1 + (2²)ⁿ = 1 + 2²ⁿ, bell one also goes off at that time so that bells 0, 1, and 2 go off together every 1+2²ⁿ seconds. Bell 3 ...