I would like to know if my answer is correct. Thanks in advanced!
A person with their head sideways in the water sees a beaver slap its tail on the lake surface 1.2 km away. What is the time difference between the sound heard in the ear listening in the air and the ear hearing the sound transmitted through the water? The speed of sound in water is 1498 m/s and the air temperature is 30 degrees celsius.
For this question I used the speed of air formula and substituted 30 degrees for T (331.4m/s + 0.606m/s/degree celsius times T) and got 349.58 m/s. After that I subtracted 1498 by 349.58 and got 1148.42. Would that be correct?
To determine the time difference between the sound heard in the air and the sound transmitted through water, there are a few steps you can follow:
1. Calculate the time it takes for sound to travel through the air:
- Use the speed of sound in air formula, which is approximately 331.4 m/s + 0.606 m/s/°C multiplied by the temperature in Celsius.
- Substituting the given temperature of 30 degrees Celsius, the speed of sound in air would be approximately 331.4 m/s + (0.606 m/s/°C * 30°C) = 349.4 m/s.
2. Calculate the time it takes for sound to travel through water:
- The given speed of sound in water is 1498 m/s.
3. Calculate the distance the sound traveled through air:
- The person with their head sideways in the water sees the beaver 1.2 km away.
- Convert 1.2 km to meters: 1.2 km * 1000 m/km = 1200 m.
4. Calculate the time it takes for the sound to travel through air using the distance and speed:
- Time = distance / speed.
- Time in air = 1200 m / 349.4 m/s ≈ 3.437 seconds.
5. Calculate the time it takes for the sound to travel through water using the distance and speed:
- Time in water = 1200 m / 1498 m/s ≈ 0.801 seconds.
6. Calculate the time difference:
- Time difference = Time in air - Time in water.
- Time difference ≈ 3.437 seconds - 0.801 seconds ≈ 2.636 seconds.
So, the time difference between the sound heard in the air and the sound transmitted through the water would be approximately 2.636 seconds.