Final answer:
The speed of sound in air at 30°C is calculated to be approximately 349 m/s. The sound takes approximately 34.38 seconds to reach the observer's ear in air and 8.01 seconds in water over a distance of 12 km, resulting in a time difference of 26.37 seconds, which does not match the provided answer choices.
The correct option is not given.
Step-by-step explanation:
The question asks for the time difference between the sound heard in the air and the sound transmitted through water. First, we must calculate the time it takes for sound to travel 12 km through air. To do this, we need to know the speed of sound in air at 30°C. The approximate speed of sound in air at 0°C is 331 m/s, and it increases by about 0.6 m/s for every degree Celsius above 0°C. At 30°C, the calculation would be:
Speed of sound in air = 331 m/s + (0.6 m/s/°C * 30°C) = 331 m/s + 18 m/s = 349 m/s.
Now we calculate the time taken for sound to travel 12 km in air and water:
- Time in air = distance/speed in air = 12,000 m / 349 m/s ≈ 34.38 s.
- Time in water = distance/speed in water = 12,000 m / 1,498 m/s ≈ 8.01 s.
The difference in time is then:
Time difference = Time in air - Time in water = 34.38 s - 8.01 s = 26.37 s.
The correct time difference does not match any of the options (a) through (d), suggesting that there may be an error in the question or answer choices.
The correct option is not given.