You are trying to overhear a juicy conversation, but from your distance of 15.0 , it sounds like only an average whisper of 35.0 . So you decide to move closer to give the conversation a sound level of 60.0 instead. How close should you come? (in cm)
Instead of posting the same question twice in one minute, you would be more likely to get help from me if you would show evidence of your own work or thought process.
I didn't mean to post the question twice and I have absolutely no idea where to start. I do not need the answer necessarily, but an equation to work with would be great. Thank you.
To determine how close you should come to achieve a sound level of 60.0 dB, you can use the inverse square law for sound intensity. According to this law, the sound intensity decreases with the square of the distance from the source.
Here are the steps to calculate the distance:
1. Use the formula for the inverse square law:
I1 / I2 = (d2 / d1)^2
where I1 and I2 are the initial and final sound intensities, and d1 and d2 are the initial and final distances.
2. Rearrange the formula to solve for d2:
d2^2 = (I1 / I2) * d1^2
3. Substitute the given values into the formula:
d2^2 = (35.0 dB / 60.0 dB) * (15.0 cm)^2
d2^2 = (0.5833) * (225.0 cm^2)
d2^2 = 131.2492 cm^2
4. Take the square root of both sides of the equation:
d2 = √(131.2492 cm^2)
d2 ≈ 11.46 cm
Therefore, you should move closer to the conversation until you are approximately 11.46 cm away to achieve a sound level of 60.0 dB.