In an experiment to measure the speed of sound in air, a boy stands 40 m from a wall and bangs two pieces of wood together. At the instant he hears the echo, he bangs them together again. He does this activity 50 times. The time taken for 50 bangs is 12 s. Which calculation gives the speed (in m `s^(-1)`) of sound in air?

Options

A. `(10)/(40xx50)`
B. `(40 xx 50)/(12)`
C. `(40xx2 xx 50)/(12)`
D. `(40xx2xx12)/(50)`

Answer

To find the speed of sound in air based on the given information, we can follow these steps:

### Step 1: Understand the Problem
The boy is standing 40 meters away from a wall and produces a sound by banging two pieces of wood together. The sound travels to the wall and back, creating an echo. The time taken for 50 bangs is 12 seconds.

### Step 2: Calculate the Time for One Bang
Since the boy bangs the wood 50 times in 12 seconds, we can find the time taken for one bang:
\[ \text{Time for one bang} = \frac{\text{Total time}}{\text{Number of bangs}} = \frac{12 \text{ s}}{50} = 0.24 \text{ s} \]

### Step 3: Calculate the Total Distance for One Echo
When the boy bangs the wood, the sound travels to the wall and back. The distance to the wall is 40 meters, so the total distance for the sound to travel (to the wall and back) is:
\[ \text{Total distance} = 2 \times \text{Distance to wall} = 2 \times 40 \text{ m} = 80 \text{ m} \]

### Step 4: Calculate the Speed of Sound
Now, we can calculate the speed of sound using the formula:
\[ \text{Speed} = \frac{\text{Total distance}}{\text{Time for one bang}} = \frac{80 \text{ m}}{0.24 \text{ s}} \approx 333.33 \text{ m/s} \]

### Final Calculation
Thus, the speed of sound in air is approximately 333.33 m/s.

### Summary of Calculation
The calculation that gives the speed of sound in air is:
\[ \text{Speed of sound} = \frac{80 \text{ m}}{0.24 \text{ s}} \approx 333.33 \text{ m/s} \]

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