A variable star is one whose brigthtness alternately increases and decrease. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average brightness of the star is 4.0, and its brightness varies by +- 0.35 magnitude. Find a function that models the brightness of Delta Cephei as a function of time.
Explain it, pls.
Thanks for your reading.
Explain it, pls.
Thanks for your reading.
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We will assume that the brightness is a sine wave y = A sin(Bt - C) + D where t is measured in days.
The period is 5.4 days/cycle. 2π/B = 5.4 days/cycle
B = 10π/27 cycles/day
The average brightness of the star is 4.0, and its brightness varies by +- 0.35 magnitude.
D = 4.0
A = 0.35
The phase shift, C, depends on where on the sine curve we want t = t0 to be. For lack of any useful information, I suppose it won't hurt to let it equal 0.
then the model of the brightness of the star is y = 0.35 sin(10 π t / 27) + 4.00. Or you could break out the calculator and say y = 0.35 sin(1.16355t) + 4.00
The period is 5.4 days/cycle. 2π/B = 5.4 days/cycle
B = 10π/27 cycles/day
The average brightness of the star is 4.0, and its brightness varies by +- 0.35 magnitude.
D = 4.0
A = 0.35
The phase shift, C, depends on where on the sine curve we want t = t0 to be. For lack of any useful information, I suppose it won't hurt to let it equal 0.
then the model of the brightness of the star is y = 0.35 sin(10 π t / 27) + 4.00. Or you could break out the calculator and say y = 0.35 sin(1.16355t) + 4.00
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trigonometry. Think about sines and cosines:
amplitude=deviation= .35
average brightness=4.0= starting point
time =5.4 days
I haven't done problems like these in 4 years but here goes:
y=.35 sin(pi*x/5.4) + 4.0
amplitude=deviation= .35
average brightness=4.0= starting point
time =5.4 days
I haven't done problems like these in 4 years but here goes:
y=.35 sin(pi*x/5.4) + 4.0