Question

Jane and Sam alternately pound a railroad spike into a tie with their hammers. The crew chief has a migraine, and notes that Jane's hammer blows cause a sound with intensity 5.0 times greater than the sound that Sam makes when he swings his hammer. What is the difference in sound level between the two sounds? answer in dB(decibels)

Answer 1

Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity (measured inW/m^2 ), in comparison to a reference level (noise).
The measure of a ratio of two sound intensities is
L₁=10 log₁₀(I₁/I₀ )
where I₁ and I₀ are the intensities.
So, we have
L₁=10 log₁₀(I₁/I₀ )=10 log₁₀(5)=10*0.6989=6.989 dB

The sound intensity level is given the letter "L₁" and is measured in "dB". The decibel is a dimensionless quantity.