Final answer:
To find the intensity level of a sound wave in air with a frequency of 53.0 Hz and an amplitude of 5.00 mm, we can calculate the intensity using the formula: I = (ρ * v * A^2 * f^2) / 2. Substituting the given values, we get an intensity level of approximately 110 dB.
Step-by-step explanation:
To find the intensity level of a sound wave, we can use the formula:
β = 10 * log(I/I0)
Where β is the intensity level in decibels, I is the intensity of the sound wave, and I0 is the reference intensity (usually taken to be 10^(-12) W/m²).
Given that the frequency of the sound wave is 53.0 Hz and the amplitude of vibration is 5.00 mm, we can calculate the intensity using the formula:
I = (ρ * v * A^2 * f^2) / 2
Where ρ is the density of air, v is the speed of sound in air, A is the amplitude of vibration, and f is the frequency of the sound wave.
Substituting the given values into the formula, we can calculate the intensity. Then, using the formula for intensity level, we can convert the intensity to decibels.
Calculating the values, we get an intensity level of approximately 110 dB.