Find the depth of sea if longitudinal waves from a ship are sent inside sea and from the bottom of sea, the waves return back after 3s. Density of water `= 10^(3) kg//m^(3)` and bulk modulus of water = 1960 x `10^6 N//m^(2)`.

Answer

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

### Step 1: Understand the problem
We need to find the depth of the sea (denoted as \(d\)) given that longitudinal waves sent from a ship return after 3 seconds. The total distance traveled by the sound waves is twice the depth (down and back up).

### Step 2: Set up the equation for distance
The total distance traveled by the sound waves is:
\[ \text{Distance} = 2d \]
Since the waves return after 3 seconds, we can express this as:
\[ 2d = v \cdot t \]
where \(v\) is the speed of sound in water and \(t\) is the time taken (3 seconds).

### Step 3: Rearrange the equation to find depth
From the equation above, we can rearrange it to find \(d\):
\[ d = \frac{v \cdot t}{2} \]

### Step 4: Calculate the speed of sound in water
The speed of sound in a medium can be calculated using the formula:
\[ v = \sqrt{\frac{B}{\rho}} \]
where \(B\) is the bulk modulus of water and \(\rho\) is the density of water. Given:
- Bulk modulus \(B = 1960 \times 10^6 \, \text{N/m}^2\)
- Density \(\rho = 10^3 \, \text{kg/m}^3\)

Substituting the values:
\[ v = \sqrt{\frac{1960 \times 10^6}{10^3}} = \sqrt{1960 \times 10^3} \]

### Step 5: Calculate \(v\)
Calculating \(v\):
\[ v = \sqrt{1960 \times 10^3} = \sqrt{1960000} \approx 1400 \, \text{m/s} \]

### Step 6: Substitute \(v\) and \(t\) into the depth equation
Now we substitute \(v\) and \(t\) into the depth equation:
\[ d = \frac{1400 \, \text{m/s} \times 3 \, \text{s}}{2} \]

### Step 7: Calculate the depth \(d\)
Calculating \(d\):
\[ d = \frac{4200}{2} = 2100 \, \text{m} \]

### Final Answer
The depth of the sea is \(d = 2100 \, \text{meters}\).

---