A source of sound has an intensity I1 and when its sound level is measured at a fixed distance the value found is 70 dB. The source then has its intensity increased to I2 and when its sound level is measured at the same distance the value found is 96 dB. What is the ratio I2/I1?Select one:a.14b.26c.600d.400
Question
A source of sound has an intensity I1 and when its sound level is measured at a fixed distance the value found is 70 dB. The source then has its intensity increased to I2 and when its sound level is measured at the same distance the value found is 96 dB. What is the ratio I2/I1?Select one:a.14b.26c.600d.400
Solution
The sound level in decibels (dB) is given by the formula:
L = 10 * log10(I/I0)
where:
- L is the sound level in dB,
- I is the intensity of the sound wave, and
- I0 is the reference intensity.
Given that the sound level for I1 is 70 dB and for I2 is 96 dB, we can set up the following equations:
70 = 10 * log10(I1/I0) ----(1) 96 = 10 * log10(I2/I0) ----(2)
We are asked to find the ratio I2/I1. To do this, we can subtract equation (1) from equation (2) to get:
96 - 70 = 10 * log10(I2/I0) - 10 * log10(I1/I0) 26 = 10 * log10(I2/I1)
Dividing both sides by 10 gives:
2.6 = log10(I2/I1)
To remove the logarithm, we can use the property of logarithms that says 10^log10(x) = x. So, we get:
10^2.6 = I2/I1
Calculating 10^2.6 gives approximately 400.
So, the ratio I2/I1 is approximately 400. Therefore, the correct answer is (d) 400.
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