There are two walls X and Y which are 120 m apart from each other. A boy standing 40 m away from wall X claps his hands once. If the speed of sound in air is 330 m `s^(-1)`, then what is the time interval between the first and the second echo that he hears?

Options

A. 0.05 s
B. 0.24 s
C. 1 s
D. 2 s

Answer

To solve the problem of finding the time interval between the first and second echo that the boy hears, we can break it down into the following steps:

### Step 1: Understand the Setup
- The boy is standing 40 m away from wall X.
- The distance between wall X and wall Y is 120 m.
- Therefore, the distance from the boy to wall Y is \(120 m - 40 m = 80 m\).

### Step 2: Calculate the Distance for Each Echo
1. **First Echo (from wall X)**:
- The sound travels from the boy to wall X and back.
- Distance to wall X = 40 m
- Distance back from wall X = 40 m
- Total distance for the first echo = \(40 m + 40 m = 80 m\).

2. **Second Echo (from wall Y)**:
- The sound travels from the boy to wall Y and back.
- Distance to wall Y = 80 m
- Distance back from wall Y = 80 m
- Total distance for the second echo = \(80 m + 80 m = 160 m\).

### Step 3: Calculate the Time Taken for Each Echo
- The speed of sound in air is given as \(330 m/s\).

1. **Time for the First Echo (from wall X)**:
\[ t_X = \frac{\text{Distance}}{\text{Speed}} = \frac{80 m}{330 m/s} = \frac{8}{33} \text{ seconds} \]

2. **Time for the Second Echo (from wall Y)**:
\[ t_Y = \frac{\text{Distance}}{\text{Speed}} = \frac{160 m}{330 m/s} = \frac{16}{33} \text{ seconds} \]

### Step 4: Calculate the Time Interval Between the Two Echoes
- The time interval \(\Delta t\) between the first and second echo is given by:
\[ \Delta t = t_Y - t_X = \frac{16}{33} - \frac{8}{33} = \frac{8}{33} \text{ seconds} \]

### Step 5: Convert to Decimal
- To convert \(\frac{8}{33}\) to decimal:
\[ \Delta t \approx 0.2424 \text{ seconds} \approx 0.24 \text{ seconds} \]

### Final Answer
The time interval between the first and second echo that the boy hears is approximately **0.24 seconds**.

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