Two students are sitting in a classroom. One is sitting in the front row 5 feet from the teacher. The second is sitting in the third row 10 feet from the teacher. The teacher's voice is measured to be 60dB at the front row. How loud will the teacher's voice be at the third row?
Question
Two students are sitting in a classroom. One is sitting in the front row 5 feet from the teacher. The second is sitting in the third row 10 feet from the teacher. The teacher's voice is measured to be 60dB at the front row. How loud will the teacher's voice be at the third row?
Solution
To answer this question, we need to understand the concept of sound intensity level or decibel level. The intensity of sound follows an inverse square law with distance. This means that the intensity of sound decreases with the square of the distance from the source.
The formula to calculate the decibel level at a certain distance is:
L2 = L1 - 20 log10(D2/D1)
where:
- L1 is the initial sound level (in dB),
- L2 is the final sound level (in dB),
- D1 is the initial distance (in feet),
- D2 is the final distance (in feet).
Given in the problem:
- L1 = 60 dB (sound level at the front row),
- D1 = 5 feet (distance of the front row from the teacher),
- D2 = 10 feet (distance of the third row from the teacher).
We can substitute these values into the formula:
L2 = 60 dB - 20 log10(10 feet / 5 feet)
Solving this equation will give us the sound level at the third row.
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