A sonic 'tape measure' is used to measure the length ofa hall. It measures a time interval of0.20 s between transmitting a sound pulse and receiving the echo. The speed of sound in air is 326 m/s. llow far is the refl ecting wall from the 'tape measure'?

Options

A. 16.3 m
B. 32.6 m
C. 48.9 m
D. 65.2 m

Explanation

To solve the problem of finding the distance to the reflecting wall using the sonic tape measure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We need to find the distance to the wall using the time taken for the sound pulse to travel to the wall and back.

2. **Identify Given Values**:
- Time interval (T) = 0.20 seconds
- Speed of sound (v) = 326 m/s

3. **Calculate the Total Distance Traveled by Sound**:
- The sound travels to the wall and back, so the total distance (D) is given by the formula:
\[ D = v \times T \]
- Substituting the values:
\[ D = 326 \, \text{m/s} \times 0.20 \, \text{s} = 65.2 \, \text{m} \]

4. **Calculate the Distance to the Wall**:
- Since the total distance includes the distance to the wall and back, we need to divide by 2 to find the one-way distance (distance to the wall):
\[ \text{Distance to the wall} = \frac{D}{2} = \frac{65.2 \, \text{m}}{2} = 32.6 \, \text{m} \]

5. **Conclusion**:
- The distance from the sonic tape measure to the reflecting wall is 32.6 meters.

### Final Answer:
The reflecting wall is 32.6 meters away from the tape measure.

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