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A noise created by small earthquake at a depth of 1200m in the ocean propagates upward and eventually reaches a bird flying above, at an altitude of 400m. Calculate how long it takes for the noise to reach the bird. For the seawater use E = 2.34 x 109 N/m2 , rho =1030kg/m3 , and for air, γ = 1.4, and T= 2700 K)

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Complete Question

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Answer:

The time taken is
t_f = 2.0 \ s

Step-by-step explanation:

Generally velocity of the noise in water is mathematically represented as


v = \sqrt{ (E)/(\rho) }

substituting into the variable with value given in the question


v = \sqrt{ (2.34 * 10^9)/(1030) }

=>
v = 1507.3 \ m/s

Generally the time taken is mathematically represented as


t = (depth )/(v)

substituting into the variable with value given in the question


t = (1200 )/(1507.3)

=>
t = 0.7961 \ s

The velocity of the noise in air is mathematically represented as


v_w = √( \gamma * T * R)

Here R is the gas constant with value
[R=286.6 m^2 /(sec^2 K) ][\tex]</p><p>So &nbsp;</p><p> &nbsp; &nbsp; &nbsp;[tex]v_w &nbsp;= &nbsp;√( 1.4 &nbsp;* &nbsp;270 &nbsp;* &nbsp;286.6)


v_w &nbsp;= &nbsp;329.1 \ &nbsp;m/s

The time taken is


t_1 = &nbsp;(400)/(329.1)

=>
t_1 = &nbsp;1.22 \ &nbsp;s

=> The total time is mathematially represented as


t_f = t_1 +t = &nbsp;1.22 + 0.7961


t_f &nbsp;= &nbsp;2.0 \ s

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