Question

The decibel reading from the television is 45. Give the corresponding intensity level. I.

45 decibels = 10^? Watts per square meter.

Give the value of the exponent. Type a decimal, round to the nearest 10th if necessary.

Answer 1

To calculate the intensity level of a sound that is at 45 decibels, you can use the decibel formula β (dB) = 10 log₁₀ (I/I₀) and solve for 'I'.

After rearranging the formula and solving, the intensity level is found to be 10⁻¹⁷ watts per square meter.

Therefore, the value of the exponent is "-17".

Step-by-step explanation:

The question asks for the intensity level of a sound that registers 45 decibels.

To find the corresponding intensity level in watts per square meter, we use the formula β (dB) = 10 log₁₀ (I/I₀), where 'I' is the sound intensity in watts per square meter and 'I₀' is the reference intensity, which is 10⁻¹² W/m² (the threshold of hearing).

First, we rearrange the formula to solve for 'I':

45 = 10 log₁₀ (I/10⁻¹²)

4.5 = log₁₀ (I/10⁻¹²)

10⁴¹⁵ = I/10⁻¹²

I = 10⁴¹⁵ × 10⁻¹²

I = 10⁻¹⁷ W/m²