An object is 11 km below sea level. A research vessel sends down a sonar signal to confirm this depth. After how long can it expect to get the echo? (Take the speed of sound in sea water as `1,520"m s"^(-1)` .)

Options

A. 15.30 s
B. 14.47 s
C. 12.20 s
D. 11.13 s

Explanation

To solve the problem of how long it takes for a sonar signal to return after being sent down to an object 11 km below sea level, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
The object is located 11 km below sea level. The sonar signal travels down to the object and then reflects back to the research vessel.

2. **Calculate the Total Distance**:
Since the sonar signal travels down to the object and back up, the total distance (D) traveled by the sonar signal is:
\[ D = 2 \times \text{depth} = 2 \times 11 \text{ km} = 22 \text{ km} \]

3. **Convert Distance to Meters**:
We need to convert kilometers to meters because the speed of sound is given in meters per second.
\[ D = 22 \text{ km} = 22 \times 1000 \text{ m} = 22000 \text{ m} \]

4. **Use the Speed of Sound**:
The speed of sound in seawater is given as \( V = 1520 \text{ m/s} \).

5. **Calculate the Time Taken for the Echo**:
We can use the formula relating distance, speed, and time:
\[ T = \frac{D}{V} \]
Substituting the values we have:
\[ T = \frac{22000 \text{ m}}{1520 \text{ m/s}} \]

6. **Perform the Calculation**:
\[ T = \frac{22000}{1520} \approx 14.47 \text{ seconds} \]

7. **Final Answer**:
The time taken for the echo to return is approximately **14.47 seconds**.