Two speakers emit sounds, the one with an intensity of 3.19 x 10^{7} \frac{W}{m^2} and the other 8.64 x 10^{8} \frac{W}{m^2}.
What is the difference in their intensity level?
\Delta \beta =
To find the difference in the intensity level between the two speakers, we need to first calculate the intensity level (β). The formula for calculating the intensity level is:
β = 10 log10(I/I₀)
where:
β is the intensity level in decibels (dB)
I is the intensity of the sound in watts per square meter (W/m²)
I₀ is the reference intensity, which is typically set at 10^{-12} W/m²
Let's calculate the intensity levels of the two speakers and then find the difference.
For the first speaker with an intensity of I₁ = 3.19 x 10^{7} W/m²:
β₁ = 10 log10(I₁/I₀)
Plugging in the values:
β₁ = 10 log10(3.19 x 10^{7} / 10^{-12})
Simplifying:
β₁ = 10 log10(3.19 x 10^{19})
Now, calculate the intensity level for the second speaker with an intensity of I₂ = 8.64 x 10^{8} W/m²:
β₂ = 10 log10(I₂/I₀)
Plugging in the values:
β₂ = 10 log10(8.64 x 10^{8} / 10^{-12})
Simplifying:
β₂ = 10 log10(8.64 x 10^{20})
Finally, calculate the difference in intensity level:
Δβ = β₂ - β₁
Plug in the calculated β values to find Δβ.