a ripple tank demonstrates the effect of two water waves being added together. the two waves are described by h = 8cos thetta t and h= 6sin thetta t,where t belongs to (0,2π) us in seconds and his the height in millimeter above still water. find the maximum height of the resultant wave and the value of t at which it occurs
Answers
The object height is placed by the above ground after considering t seconds and given by the function h(t) is 144 and raise according to the ripple function.
This should be calculated in achieving over integration and integrate over either t=-2t and follows basic rules.
The properties are consider and add to H values.
Given : a ripple tank demonstrates the effect of two water waves being added together. the two waves are described by h = 8cos t and h= 6sin t, where t belongs to (0,2π) us in seconds and the height in millimeter above still water.
To find : the maximum height of the resultant wave and the value of t at which it occurs
Solution:
h = 8cost
h = 6sint
added together.
8cost + 6sint
Maximum value of acosx + bsinx is given by √a²+b²
Hence maximum value = √8² + 6² = 10
maximum height of the resultant wave = 10
(10/10)( 8cost + 6sint)
= 10 ( (4/5)cost + (3/5)Sint)
4/5 = cosa then 3/5 = Sina
=> a = Cos⁻¹(4/5) or Sin⁻¹(3/5)
= 10 ( cos a Cost + sinasint)
= 10 ( cos ( a - t)
is max when
a - t = 0
=> t = a
=> t = Cos⁻¹(4/5) or Sin⁻¹(3/5)
=> t ≈ 37° ≈ 0.21π
maximum height of the resultant wave = 10 mm
and the value of t at which it occurs = 37° ≈ 0.21π
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