Question

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)

Answer 1

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  </p><p>      [tex]v_w  =  √( 1.4  *  270  *  286.6)`

`v_w  =  329.1 \  m/s`

The time taken is

`t_1 =  (400)/(329.1)`

=>
`t_1 =  1.22 \  s`

=> The total time is mathematially represented as

`t_f = t_1 +t =  1.22 + 0.7961`

`t_f  =  2.0 \ s`