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Thread: Siren wave

  1. #1
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    Siren wave

    I have done the attached question but I don't entirely understand it. I used degrees but is there any reason to not use radians? How long is the wave period in minutes?
    Attached Thumbnails Attached Thumbnails Siren wave-scan-1.jpg  
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  2. #2
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    I don't think the length of a wave is given or needed. Only percentages of a wave above certain y values are calculated.
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  3. #3
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    (a), at least, is very easy: the maximum value of sin(x) is 1 and the minimum value is -1.

    For (b), you are asking when 20 sin(6t)+ 70> 75 which is the same as asking when sin(6t)> 5/20= 1/4. Determine the value of 6t (you don't need or want t) for which sin(6t)= 1/4 and check to see which intervals give ">" and which "<". Divide the length of the correct interval by 360 (if you use degrees) or by $\displaystyle 2\pi$ if you use radians.

    For (c), use the same method as (b) except "in reverse". 45% of 360 is 162 so you want A sin(6t)+ 70= 75, or sin(6t)> -5/A for a difference of 6t= 162(6)= 972 degrees.
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  4. #4
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    Yes, I said I'd done the question. I see now I don't need t. I could have used x instead in my working to show that x and t are different.
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  5. #5
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    The 6 isn't needed either. Its an unusual question.
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