The ultrasonic waves take 4 seconds to travel from the ship to the bottom of the sea and back to the ship (in the form of an echo). What is the depth of the sea? (Speed of sound in water = 1500 m/s.)

Options

A. 3000 m
B. 2000 m
C. 1000 m
D. 500 m

Explanation

To find the depth of the sea using the information provided, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
The ultrasonic waves take 4 seconds to travel to the bottom of the sea and back to the ship. This means the total time for the sound to travel down and then back up is 4 seconds.

2. **Identify the Given Values**:
- Speed of sound in water (v) = 1500 m/s
- Total time taken (t) = 4 seconds

3. **Determine the Distance Travelled**:
The sound wave travels to the bottom of the sea and back, which means it covers twice the depth of the sea. If we let the depth of the sea be \( x \), then the total distance travelled by the sound wave is \( 2x \).

4. **Use the Formula for Distance**:
The formula for distance is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the distance travelled by the sound wave is \( 2x \), so we can write:
\[ 2x = v \times t \]

5. **Substitute the Known Values**:
Substitute the values of \( v \) and \( t \) into the equation:
\[ 2x = 1500 \, \text{m/s} \times 4 \, \text{s} \]

6. **Calculate the Total Distance**:
Calculate the right side of the equation:
\[ 2x = 1500 \times 4 = 6000 \, \text{m} \]

7. **Solve for Depth (x)**:
Now, to find the depth \( x \), divide both sides by 2:
\[ x = \frac{6000}{2} = 3000 \, \text{m} \]

8. **Conclusion**:
The depth of the sea is \( 3000 \, \text{meters} \).

### Final Answer:
The depth of the sea is **3000 meters**.

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