Final answer:
The sound intensity level for a sound wave of intensity 6.0×10⁻⁸ W/m² is calculated using the formula L = 10 × log10(I / I0), which results in approximately 47.78 dB.
Step-by-step explanation:
To calculate the sound intensity level in decibels (dB) for a given sound intensity in watts per meter squared (W/m²), we use the formula:
L = 10 × log10(I / I0)
where L is the sound intensity level in decibels, I is the sound intensity in W/m², and I0 is the reference sound intensity, typically set at 10⁻¹² W/m², which is the standard threshold of hearing.
Using the given sound intensity of 6.0×10⁻⁸ W/m², the calculation would be as follows:
L = 10 × log10(6.0×10⁻⁸ / 10⁻¹²) = 10 × log10(6.0×10⁴) = 10 × (log10(6) + log10(10⁴))
L = 10 × (0.778 + 4) = 10 × 4.778 = 47.78 dB
Therefore, the sound intensity level for a sound wave of intensity 6.0×10⁻⁸ W/m² is approximately 47.78 dB.