Determine the change in intensity level (in decibels) when a sound intensity is increased by a factor of 2.0, 20, 200.
To determine the change in intensity level in decibels when a sound intensity is increased by a certain factor, we can use the formula:
ΔL = 10 * log10(factor)
Where ΔL is the change in intensity level in decibels and factor is the given increase in intensity.
Let's calculate the change in intensity level for each given factor:
1. When the factor is 2.0:
ΔL = 10 * log10(2.0)
ΔL ≈ 3.0103 decibels
2. When the factor is 20:
ΔL = 10 * log10(20)
ΔL ≈ 13.9794 decibels
3. When the factor is 200:
ΔL = 10 * log10(200)
ΔL ≈ 23.0103 decibels
Therefore, the change in intensity level in decibels for an increase by a factor of 2.0 is approximately 3.0103 decibels, for an increase by a factor of 20 is approximately 13.9794 decibels, and for an increase by a factor of 200 is approximately 23.0103 decibels.
To determine the change in intensity level in decibels when the sound intensity is increased by a certain factor, we can use the formula:
ΔL = 10 * log10(I2 / I1)
Where:
ΔL is the change in intensity level in decibels.
I1 is the initial sound intensity.
I2 is the final sound intensity.
Let's calculate the change in intensity level for each case.
1. When the sound intensity is increased by a factor of 2.0:
Here, I2 is 2 times the value of I1.
ΔL = 10 * log10(2.0 * I1 / I1)
ΔL = 10 * log10(2.0)
Using a calculator, we find that ΔL ≈ 3.0103 decibels.
2. When the sound intensity is increased by a factor of 20:
Here, I2 is 20 times the value of I1.
ΔL = 10 * log10(20 * I1 / I1)
ΔL = 10 * log10(20)
Using a calculator, we find that ΔL ≈ 13.0103 decibels.
3. When the sound intensity is increased by a factor of 200:
Here, I2 is 200 times the value of I1.
ΔL = 10 * log10(200 * I1 / I1)
ΔL = 10 * log10(200)
Using a calculator, we find that ΔL ≈ 23.0103 decibels.
Therefore, the change in intensity level (in decibels) when the sound intensity is increased by a factor of 2.0, 20, and 200 is approximately 3.0103 dB, 13.0103 dB, and 23.0103 dB respectively.