1. A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.50 s later. Find the depth of the well if the air temperature is 10.0°C.
2. Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2
I will be happy to critique your thinking or work.
To solve these problems, I'll need to explain the relevant formulas and concepts.
1. To find the depth of the well, we can use the equation for the time it takes for an object to fall from an initial height:
t = sqrt(2h / g)
Where:
t is the time taken (1.50 s)
h is the height or depth of the well (what we need to find)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Rearranging the formula, we can solve for h:
h = (1/2) * g * t^2
Plugging in the values we know:
h = (1/2) * 9.8 m/s^2 * (1.50 s)^2
h = 11.025 m
Hence, the depth of the well is approximately 11.025 meters.
2. To calculate the sound level in decibels, we need to use the formula:
L = 10 * log10(I / I0)
Where:
L is the sound level in decibels
I is the sound wave intensity in watts per square meter (2.25 µW/m^2, which is equivalent to 2.25 x 10^-6 W/m^2)
I0 is the reference intensity, which is the threshold of hearing (I0 = 1 x 10^-12 W/m^2)
Plugging in the values we know:
L = 10 * log10(2.25 x 10^-6 W/m^2 / 1 x 10^-12 W/m^2)
L = 10 * log10(2.25 x 10^6)
Using a calculator, we find:
L ≈ 66 dB
Therefore, the sound level of the sound wave is approximately 66 decibels.