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
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To solve these problems, we can use the relevant formulas and concepts from physics.
1. To find the depth of the well, we can use the equation of motion for an object in free fall:
h = (1/2)gt^2
where h is the depth of the well, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time it takes for the sound to travel back up the well.
In this case, the time is given as 1.50 s. Plugging in the values, we have:
h = (1/2) * 9.8 m/s^2 * (1.50 s)^2
h = 11.025 m
Therefore, the depth of the well is approximately 11.025 meters.
2. To calculate the sound level in decibels (dB), we can use the formula:
L = 10 * log10(I/I0)
where L is the sound level in decibels, I is the sound intensity, and I0 is the reference intensity. The reference intensity is typically defined as the threshold of hearing, which is 1 x 10^(-12) W/m^2.
In this case, the sound intensity is given as 2.25 µW/m^2, which is equal to 2.25 x 10^(-6) W/m^2. Plugging in the values, we have:
L = 10 * log10((2.25 x 10^(-6)) / (1 x 10^(-12)))
L = 10 * log10(2.25 x 10^6)
Now, we can calculate the logarithm using a scientific calculator or logarithm table:
L ≈ 10 * 6.352
L ≈ 63.52 dB
Therefore, the sound level of the given sound wave is approximately 63.52 decibels.