Hi, can you help me with this one?
A family ice show is held in an enclosed arena. The skaters perform to music playing at a level of 75.0 dB. This intensity level is too loud for your baby, who yells at 65.5 dB.
(a) What total sound intensity engulfs you?
_____ W/m2
(b) What is the combined sound level?
____ dB
I will be happy to critique your thinking on this. Your posting many questions under differing names is a questionable practice, if you are seeking help.
I will be happy to critique your thinking on this. Your posting many questions under differing names is a questionable practice, if you are seeking help.
To find the total sound intensity, we need to use the formula for sound intensity level in decibels:
I = 10^((L/10) - 12)
where I is the sound intensity in watts per square meter (W/m^2) and L is the sound level in decibels (dB).
(a) To find the total sound intensity engulfs you, we need to add the individual sound intensities of the family ice show and the baby's yell. Since sound intensities add up logarithmically, we can use the formula:
I_total = I_show + I_baby
First, let's convert the sound levels to sound intensities using the formula mentioned above:
I_show = 10^((75.0/10) - 12)
I_baby = 10^((65.5/10) - 12)
Now, we can calculate the total sound intensity:
I_total = I_show + I_baby
(b) To find the combined sound level, we need to use the formula:
L_combined = 10log(I_total/10^(-12))
Now, let's substitute the calculated values into the formulas to find the solutions.
To determine the total sound intensity and the combined sound level in this scenario, we need to use the principles of sound intensity and sound level.
(a) To find the total sound intensity, we need to consider that sound intensity is measured in watts per square meter (W/m^2). The intensity level of a sound is calculated using the formula:
I = I₀ * 10^(L/10)
Where:
- I is the sound intensity in W/m^2
- I₀ is the reference intensity, which is typically 10^(-12) W/m^2
- L is the sound level in decibels (dB)
For the skaters performing to music at a level of 75.0 dB, we can find the sound intensity using the formula. Let's calculate:
I₁ = I₀ * 10^(L₁/10)
= 10^(-12) * 10^(75/10)
= 10^(-12) * 10^7.5
≈ 3.162 * 10^(-6) W/m^2
For the baby yelling at 65.5 dB, we can find the sound intensity in the same manner:
I₂ = I₀ * 10^(L₂/10)
= 10^(-12) * 10^(65.5/10)
= 10^(-12) * 10^6.55
≈ 1.995 * 10^(-7) W/m^2
To find the total sound intensity, we can sum up the individual sound intensities:
Total sound intensity = I₁ + I₂
= 3.162 * 10^(-6) + 1.995 * 10^(-7)
≈ 3.361 * 10^(-6) W/m^2
Therefore, the total sound intensity engulfing you is approximately 3.361 * 10^(-6) W/m^2.
(b) Now let's determine the combined sound level. The combined sound level in decibels is calculated using the formula:
L_combined = 10 * log₁₀(I_combined / I₀)
Where:
- L_combined is the combined sound level
- I_combined is the combined sound intensity
- I₀ is the reference intensity, which is typically 10^(-12) W/m^2
Using the total sound intensity found in part (a), we can calculate the combined sound level:
L_combined = 10 * log₁₀(I_total / I₀)
= 10 * log₁₀(3.361 * 10^(-6) / 10^(-12))
= 10 * log₁₀(3.361 * 10^(6))
≈ 97.24 dB
Therefore, the combined sound level is approximately 97.24 dB.