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)
Complete Question
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Answer:
The time taken is [tex] t_f = 2.0 \ s [/tex]
Explanation:
Generally velocity of the noise in water is mathematically represented as
[tex]v = \sqrt{ \frac{E}{\rho} }[/tex]
substituting into the variable with value given in the question
[tex]v = \sqrt{ \frac{2.34 * 10^9}{1030} }[/tex]
=> [tex]v = 1507.3 \ m/s [/tex]
Generally the time taken is mathematically represented as
[tex]t = \frac{depth }{v}[/tex]
substituting into the variable with value given in the question
[tex]t = \frac{1200 }{1507.3}[/tex]
=> [tex]t = 0.7961 \ s [/tex]
The velocity of the noise in air is mathematically represented as
[tex]v_w = \sqrt{ \gamma * T * R}[/tex]
Here R is the gas constant with value [tex] [R=286.6 m^2 /(sec^2 K) ][\tex]
So
[tex]v_w = \sqrt{ 1.4 * 270 * 286.6}[/tex]
[tex]v_w = 329.1 \ m/s [/tex]
The time taken is
[tex] t_1 = \frac{400}{329.1}[/tex]
=> [tex] t_1 = 1.22 \ s[/tex]
=> The total time is mathematially represented as
[tex] t_f = t_1 +t = 1.22 + 0.7961 [/tex]
[tex] t_f = 2.0 \ s [/tex]