Question

Q/C An undersea earthquake or a landslide can produce an ocean wave of short duration carrying great energy, called a tsunami. When its wavelength is large compared to the ocean depth d, the speed of a water wave is given approximately by v = √(gd). Assume an earthquake occurs all along a tectonic plate boundary running north to south and produces a straight tsunami wave crest moving everywhere to the west. (c) If the wave has amplitude 1.80 m when its speed is 200 m/s, what will be its amplitude where the water is 9.00 m deep?

Answer 1

The amplitude $A_{2}$ is 8.307 m

When describing the peak value of a quantity, such as the level of sound waves or the power and voltage in electrical and electronic systems, the term amplitude is employed. A louder sound has a bigger amplitude, and a softer sound has a smaller amplitude.

As we previously discussed in the concept session, the square root of the water's speed is inversely related to the amplitude of its waves.

$A\alpha\frac{1}{\sqrt{v} }$

Solve for first case:

$A_{1}=\frac{1}{\sqrt{v_{1} } }$

Solve for second case:

$A_{2}=\frac{1}{\sqrt{v_{2} } }$

So, the two equations is equal

$A^{2} _{1} v_{1} = A^{2} _{2} v_{2}$

        $=A^{2} _{2} \sqrt{g d_{2} }$

Rearrange and solve for the amplitude $A_{2}$ :

$A_{2} =\sqrt{\frac{A^{2}_{1} v_{1} }{v_{2} } }$

    $=\sqrt{\frac{A^{2}_{1} v_{1} }{\sqrt{g d_{2} } } }$

    $=\sqrt{\frac{(1.8m)^{2} X200 m/s }{\sqrt{9.8m/s^{2}X9 m } } }$

    = 8.307 m

So, The amplitude $A_{2}$ is 8.307 m.

Learn more about amplitude here:

brainly.com/question/3613222

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