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?
in air ,
v = 331.4m/s + 0.606m/s/degree celsius times T
= 331.4 + .606(30)
= 349.58 m/s
time to travel 1.2 km
= 1200/349058 = 3.4327 seconds
in water:
time = 1200/1498 = .801 seconds
time difference = 3.4327 - .801 or 2.63 seconds
for yours, ok, so far, but you have not yet considered the time.
you found the difference in the speeds.
You did not even consider the fact that the distance was 1.2 km.
( I am assuming your formula is correct, and that the temperature does not affect the speed of sound in water. Common sense tells me it should)
Hmm, let me think about this for a moment.
Well, it seems you're on the right track with finding the speed of sound in air at 30 degrees Celsius. However, I'm afraid there's a slight mix-up in your calculations.
The speed of sound in air can be calculated using the formula:
speed = 331.4 m/s + 0.606 m/s/°C * temperature.
Substituting the temperature of 30 degrees Celsius, we get:
speed = 331.4 m/s + 0.606 m/s/°C * 30 °C.
Simplifying this equation, we find:
speed = 331.4 m/s + 18.18 m/s = 349.58 m/s.
So, it seems you've correctly determined the speed of sound in air at 30 degrees Celsius. However, to find the time difference between the sound in air and in water, we need to consider the distance the sound travels through each medium.
The time it takes for the sound to travel through air can be calculated using the formula:
time = distance / speed.
In this case, the distance is given as 1.2 km, which is equal to 1200 m. So, the time it takes for the sound to travel through air is:
time_air = 1200 m / 349.58 m/s.
Using simple division, we find:
time_air ≈ 3.43 seconds.
Now, let's consider the time it takes for the sound to travel through water. The distance is still 1.2 km, but the speed of sound in water is given as 1498 m/s.
So, the time it takes for the sound to travel through water is:
time_water = 1200 m / 1498 m/s.
Calculating this, we find:
time_water ≈ 0.801 seconds.
To find the time difference between the sound heard in air and in water, we subtract the time it takes for the sound to travel through air from the time it takes for the sound to travel through water:
time_difference = time_water - time_air.
Substituting the values we found earlier, we have:
time_difference ≈ 0.801 seconds - 3.43 seconds.
Now, I don't want to subtract the fun from your calculations, but this subtraction isn't possible since the time it takes for the sound to travel through water is actually less than the time it takes through air. So, the resulting time difference will be negative. You might need to double-check your calculations to ensure accuracy.
Remember, when it comes to the difference between sound in air and water, there's no need to dive too deep into those calculations. It's enough to say that sound travels faster through water than through air.
To find the time difference between the sound heard in the air and the sound transmitted through the water, you need to calculate the time it takes for sound to travel in both mediums separately.
First, let's calculate the time it takes for sound to travel in the air:
Given the distance (1.2 km) and the speed of sound in air at a temperature of 30 degrees Celsius (331.4 m/s + 0.606 m/s/degree Celsius * 30), we can use the formula:
Time = Distance / Speed
Time in air = (1.2 km) / (349.58 m/s)
Note: Convert the distance to meters (1.2 km = 1200 m) to ensure consistent units.
Time in air = 1200 m / 349.58 m/s
Time in air ≈ 3.43 seconds
Next, let's calculate the time it takes for sound to travel in water:
Given the distance (1.2 km) and the speed of sound in water (1498 m/s), we can again use the formula:
Time = Distance / Speed
Time in water = (1.2 km) / (1498 m/s)
Again, convert the distance to meters:
Time in water = 1200 m / 1498 m/s
Time in water ≈ 0.801 seconds
Finally, to find the time difference between the two, subtract the time in water from the time in air:
Time difference = Time in air - Time in water
Time difference ≈ 3.43 seconds - 0.801 seconds
Time difference ≈ 2.629 seconds
So, the time difference between the sound heard in the air and the ear hearing the sound transmitted through the water is approximately 2.629 seconds.
To find the time difference between the sound heard in the air and the sound transmitted through water, you need to consider the different speeds of sound in air and water.
To calculate the speed of sound in air at a given temperature, you can use the formula:
V_air = 331.4 + 0.606 * T
- Where V_air is the speed of sound in air in m/s.
- T is the temperature in degrees Celsius.
So, at a temperature of 30 degrees Celsius, the speed of sound in air can be calculated as:
V_air = 331.4 + 0.606 * 30 = 331.4 + 18.18 = 349.58 m/s.
You correctly calculated the speed of sound in air at the given temperature as 349.58 m/s.
To find the time difference, you need to find the difference in time it takes sound to travel 1.2 km in air and water.
Let's calculate the time it takes for sound to travel 1.2 km in air:
Time_air = distance / speed = 1200 m / 349.58 m/s = 3.43 seconds (approximately).
Now, let's calculate the time it takes for sound to travel 1.2 km in water:
Time_water = distance / speed_water = 1200 m / 1498 m/s = 0.801 seconds (approximately).
To find the time difference, subtract the time taken in water from the time taken in air:
Time_difference = Time_air - Time_water = 3.43 s - 0.801 s = 2.629 seconds (approximately).
So, the time difference between the sound heard in air and the sound transmitted through water is approximately 2.629 seconds.
In conclusion, your calculation of the speed of sound in air was correct, but you forgot to calculate the time taken in water and subtract it from the time taken in air to find the time difference.