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

Δβ = 7 dB

Explanation:

For this exercise we must find the difference in sound level in beta. The sound level is defined by

         β = 10 log (I / I₀)

They indicate that Jane's intensity (I₁) is 5 times greater than Sam's intensity (I₂)

          I₁ = 5 I₂

Let's look for the level of each one and subtract it

      β₁ = 10 log (I₁ / I₀)

      β₂ = 10 log (I₂ / I₀)

      β₁ - β₂ = 10 (log (I₁ / I₀) - log (I₂ / I₀))

      β₁ - β₂ = 10 log (I₁ / I₂)

      β₁ - β₂ = 10 log (5)

      β₁ -β₂ = 7 dB

      Δβ = 7 dB

thermal energy is the answer