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Math Help - 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 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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