When a compressible wave is sent towards bottom of sea from a stationary ship it is observed that its echo is hear after `2s`. If bulk modulus of elasticity of water is `2xx10^(9)N//m^(2)`, mean temperature of water is `4^(@)` and mean density of water is `1000kg//m^(3)`, then depth of sea will be

Options

A. `1014m`
B. `1414m`
C. `2828m`
D. `3000m`

Explanation

To solve the problem of finding the depth of the sea based on the given information, we can follow these steps:

### Step 1: Understand the Problem
When a sound wave is sent from a stationary ship to the bottom of the sea, it travels down to the seabed and reflects back to the ship. The total time taken for this journey is given as 2 seconds.

### Step 2: Relate Time to Distance and Speed
The total distance traveled by the sound wave is twice the depth of the sea (down and back up). We can express this relationship mathematically:
\[ \text{Total Distance} = 2D \]
where \(D\) is the depth of the sea.

The time taken for this journey is given as 2 seconds. Therefore, we can write:
\[ \frac{2D}{V_s} = 2 \]
where \(V_s\) is the speed of sound in water.

### Step 3: Solve for Depth
From the equation above, we can simplify it:
\[ 2D = 2V_s \implies D = V_s \]
So, we need to find the speed of sound in water, \(V_s\).

### Step 4: Calculate the Speed of Sound in Water
The speed of sound in a liquid can be calculated using the formula:
\[ V_s = \sqrt{\frac{\beta}{\rho}} \]
where:
- \(\beta\) is the bulk modulus of elasticity (given as \(2 \times 10^9 \, \text{N/m}^2\)),
- \(\rho\) is the density of the liquid (given as \(1000 \, \text{kg/m}^3\)).

Substituting the values:
\[ V_s = \sqrt{\frac{2 \times 10^9}{1000}} \]

### Step 5: Perform the Calculation
Calculating the above expression:
\[ V_s = \sqrt{2 \times 10^6} = \sqrt{2000000} \approx 1414.21 \, \text{m/s} \]

### Step 6: Find the Depth
Since we established that \(D = V_s\), we have:
\[ D \approx 1414.21 \, \text{m} \]

### Final Answer
Thus, the depth of the sea is approximately:
\[ D \approx 1414 \, \text{meters} \]