A bell is rung at a sound intensity of 70dB . A trumpet is blown at an intensity that is greater by a factor of 10^3. What is the intensity level of the trumpet
I bet it is 10log1000 greater than 70db
To find the intensity level of the trumpet, we need to compare it to a reference intensity level of 0 dB.
Given that the bell is rung at an intensity level of 70 dB, the trumpet's intensity level is greater by a factor of 10^3.
Here's how we can calculate the intensity level of the trumpet:
Step 1: Use the formula for intensity level in decibels:
Intensity Level (dB) = 10 * log10(I1 / I0)
where I1 is the intensity being measured and I0 is the reference intensity level (0 dB).
Step 2: Substitute the values into the formula:
I1 = 10^3 * I0 (because the trumpet's intensity is greater by a factor of 10^3)
Intensity Level (trumpet, dB) = 10 * log10(10^3 * I0 / I0)
Step 3: Simplify the equation:
Intensity Level (trumpet, dB) = 10 * log10(10^3)
Step 4: Evaluate the logarithm:
Intensity Level (trumpet, dB) = 10 * 3
Step 5: Perform the multiplication:
Intensity Level (trumpet, dB) = 30
Therefore, the intensity level of the trumpet is 30 dB.
To find the intensity level of the trumpet, we need to understand the relationship between intensity and intensity level, which is measured in decibels (dB). The formula to calculate the intensity level (IL) in decibels is:
IL = 10 * log10(I/I₀)
Where:
- IL: Intensity level in decibels
- I: Intensity of the sound
- I₀: Reference intensity (typically the threshold of hearing, which is approximately 10^−12 W/m²)
Since the question provides the sound intensity of the bell at 70 dB, we can use it to find the reference intensity (I₀).
70 dB = 10 * log10(I/I₀)
Divide both sides of the equation by 10:
7 = log10(I/I₀)
Rewrite the equation in exponential form:
I/I₀ = 10^7
Now we can calculate the reference intensity (I₀):
I₀ = I/10^7
Given that the trumpet is blown at an intensity 10^3 times greater than the bell, we can express the intensity of the trumpet (I_trumpet) relative to the intensity of the bell (I_bell):
I_trumpet = 10^3 * I_bell
I_trumpet = 10^3 * (I₀ * 10^7) (substituting I₀)
Now we can calculate the intensity level of the trumpet (IL_trumpet) using the formula:
IL_trumpet = 10 * log10(I_trumpet/I₀)
IL_trumpet = 10 * log10((10^3 * (I₀ * 10^7))/I₀)
Simplifying the expression:
IL_trumpet = 10 * log10(10^3 * 10^7) (canceling I₀)
IL_trumpet = 10 * log10(10^10)
Applying the logarithmic rule:
IL_trumpet = 10 * 10 = 100 dB
Therefore, the intensity level of the trumpet is 100dB.