The ratio of intensities of sounds A
and B is 100: 1, then the intensity
level of A is greater than that of B
(a) 100 times (b) 10 times
(c) 2 times (d) 2 times
Answers
(a) 100 Times
is a correct answer
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The intensity level of A is greater than that of B by 20 times.
Given: The ratio of intensities of sounds A and B is 100: 1.
To Find: The intensity level of A that is greater than that of B.
Solution:
- We know that the other name for intensity level is loudness.
- Loudness can be calculated using the formula,
Δ L = 10 × log ( I1 / I2 ) ...(1)
Where Δ L = change in loudness, I1 = intensity of A, I2 = intensity of B.
Coming to the numerical,
let the intensity of A be ' I1 '
and let the intensity of B be ' I2 '.
So, we are given that,
I1 / I2 = 100
So, putting respective values in (1), we get;
Δ L = 10 × log ( I1 / I2 )
⇒ Δ L = 10 × log 100
⇒ Δ L = 10 × log 10²
⇒ Δ L = 10 × 2 log 10
⇒ Δ L = 20
So, the intensity level of A is greater than that of B by 20 times.
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