It takes 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is `10^(@) C`. If the temperature rise to `30 ^(@)C` the sound wave travels between the same fixed parts in

Options

A. 1.9 s
B. 2.0 s
C. 2.1 s
D. 2.2 s

Answer

To solve the problem, we need to determine the time it takes for a sound wave to travel between two fixed points when the temperature changes from 10°C to 30°C. We will use the relationship between the speed of sound and temperature.

### Step-by-Step Solution:

1. **Understand the relationship between temperature and speed of sound**:
The speed of sound in air increases with temperature. The formula for the speed of sound \( v \) in air is given by:
\[ v = 331 + 0.6T \]
where \( T \) is the temperature in degrees Celsius.

2. **Calculate the speed of sound at 10°C**:
\[ v_1 = 331 + 0.6 \times 10 = 331 + 6 = 337 \, \text{m/s} \]

3. **Calculate the speed of sound at 30°C**:
\[ v_2 = 331 + 0.6 \times 30 = 331 + 18 = 349 \, \text{m/s} \]

4. **Determine the distance between the two fixed points**:
Since it takes 2 seconds for the sound to travel between the two points at 10°C, we can calculate the distance \( L \):
\[ L = v_1 \times t = 337 \, \text{m/s} \times 2 \, \text{s} = 674 \, \text{m} \]

5. **Calculate the time taken to travel the same distance at 30°C**:
Using the speed of sound at 30°C, we can find the new time \( t_2 \):
\[ t_2 = \frac{L}{v_2} = \frac{674 \, \text{m}}{349 \, \text{m/s}} \approx 1.93 \, \text{s} \]

6. **Final answer**:
The time taken for the sound wave to travel between the same fixed points at 30°C is approximately:
\[ t_2 \approx 1.93 \, \text{s} \]