The sound level, measured in decibels (dB), is a logarithmic scale that quantifies the intensity or loudness of sound. The relationship between sound level and pressure amplitude is logarithmic in nature.
The formula to calculate the change in sound level (ΔL) given the ratio of two pressure amplitudes (P₁ and P₂) is:
ΔL = 20 * log₁₀(P₂ / P₁)
To determine the factor by which the pressure amplitude is increased when the sound level increases from 50 dB to 60 dB, we can rearrange the formula to solve for the pressure ratio (P₂ / P₁):
P₂ / P₁ = 10^(ΔL / 20)
Here, ΔL is the difference in sound level between the two cases, which is 60 dB - 50 dB = 10 dB. Plugging this value into the formula, we get:
P₂ / P₁ = 10^(10 / 20) = 10^0.5 ≈ 3.162
Therefore, the pressure amplitude is increased by a factor of approximately 3.162 when the sound level is increased from 50 dB to 60 dB.