A variable star is one whose brightness alternately increases and decr

hionormf 2021-12-18 Answered
A variable star is one whose brightness alternately increases and decreases. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average brightness (or magnitude) 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.
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Expert Answer

chumants6g
Answered 2021-12-19 Author has 33 answers

Step 1
Start with a sine function, that has average value 0, magnitude ±1, period 2π
f(t)=sin
To make the period 5.4 days, multiply t by 2π5.4
f(t)=sin(2π5.4t)
Now whenever t is a multiple of 5.4, it will be the sine of an integer multiple of 2π
Step 2
The make the average value (the center horizontal line that the sine function moves back and forth over) 4.0, add to the function 4.0, It shifts the graph up by 4 units
f(t)=4+sin(2π5.4t)
Step 3
To change the magnitude to ±0.35 multiply the sine by 0.35. Since the sine bounces back and forth between -1 and 1, this makes it so it bounces back and forth between -0.35 and 0.35
f(t)=4+0.35sin(2π5.4t)
Since they don't give any information about what the brightness should be at a specific time, we don't need to add or subtract anything from t to horizontally shift the graph.

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Lakisha Archer
Answered 2021-12-20 Author has 39 answers
Step 1
Rajdeep, First, lets

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nick1337
Answered 2021-12-27 Author has 575 answers

Step 1
NSK
There are many functions that alternately increase and decrease (called periodic functions), but the simplest of these is the sine function,
y=Asin(2πT)tϕ)+b
Here y and t are the variables: magnitude and time in your case.
A is called the amplitude; it tells us the maximum variation of y. In your case, A = 0.35.
T is called the period; it tells us the duration of one cycle. In your case, T = 5.4 days.
b is the off-set in the y-direction, or average value of y. In your case, b = 4.4.
ϕ is called the phase shift; it tells us by how much the initial value of y is off-set from the average value, y=b. In your case
ϕ=0
Putting it all in, you get
y=0.35sin((2π5.4)t)+4.4

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