A member of an aircraft maintenance crew wears protective earplugs that reduce the sound intensity by a factor of 355. When a jet aircraft is taking off, the sound intensity level experienced by the crew member is 72 dB. What sound intensity level would the crew member experience if he removed the protective earplugs?
what is log 355? 2.55
multiply that by 10, add it to 72 db
intensity= 10 log (power)=10log(original)+10log355
A factor of 355 in intensity is 25.5 dB more than 72 dB. That makes 97.5 dB
Here's how I got that: Take 10 times the log(base10) of 355.
To find the sound intensity level experienced by the aircraft maintenance crew member without the earplugs, we need to understand the concept of sound intensity and how it relates to the decibel (dB) scale.
The decibel scale is a logarithmic scale that measures the intensity of a sound relative to a reference level. It is important to note that the decibel scale is logarithmic because the human ear perceives sound intensity in a logarithmic manner.
Since the earplugs reduce the sound intensity by a factor of 355, we can deduce that the sound intensity with the earplugs is 1/355th (or 1/355 times) of the sound intensity without the earplugs.
Now, let's calculate the sound intensity level experienced by the crew member without the earplugs:
1. Convert the given sound intensity level into sound intensity:
- The formula to convert sound intensity level (L) to sound intensity (I) is:
I = 10^((L - L₀)/10)
- Here, L₀ is the reference sound intensity level, which is typically set at the threshold of human hearing and is equal to 0 dB.
- In this scenario, the sound intensity with the earplugs can be calculated as:
I₁ = 10^((72 - 0)/10)
2. Calculate the sound intensity without the earplugs using the reduced factor:
- Since the sound intensity with the earplugs is 1/355th of the sound intensity without the earplugs, we can write the equation as:
I₂ = 1/355 * I₁
3. Convert the sound intensity back into sound intensity level:
- Using the same formula as step 1, we can calculate the sound intensity level without the earplugs:
L₂ = 10 * log10(I₂/L₀)
4. Calculate the sound intensity level without the earplugs:
- Plug in the values into the formula:
L₂ = 10 * log10((1/355 * I₁)/L₀)
Remember to use a calculator capable of performing logarithmic calculations.
By following these steps, you should be able to find the sound intensity level that the crew member would experience if the protective earplugs were removed.