Final answer:
To calculate the power output of the speaker, convert the sound intensity level from decibels (dB) to watts per meter squared (W/m²) using the formula I = 10^(L/10), where I is the sound intensity in W/m² and L is the sound intensity level in dB. Then, calculate the power output using the formula P = I * A, where P is the power output in watts, I is the intensity in W/m², and A is the surface area of the speaker.
Step-by-step explanation:
To calculate the power output of the speaker, we need to convert the sound intensity level from decibels (dB) to watts per meter squared (W/m²).
First, we calculate the sound intensity by using the formula:
I = 10^(L/10)
where I is the sound intensity in W/m² and L is the sound intensity level in dB. Given that the sound intensity level is 105 dB, we can plug this value into the formula to find the intensity.
I = 10^(105/10) = 10^10.5 ≈ 316227.766 W/m²
Next, we can calculate the power output of the speaker by using the formula:
P = I * A
where P is the power output in watts, I is the intensity in W/m², and A is the surface area of the speaker.
Since the problem does not provide the surface area of the speaker, we cannot calculate the exact power output.