A sound wave in water has an intensity of 1.00 $\times$ 10^-3 Watts/m².The density of water is 1,000 kg/m³ and the velocity of sound in water is 1,482 m/s.The pressure amplitude of the sound wave is A) 60.2 N/m². B) 54.4 N/m². C) 49.5 N/m². D) 42.5 N/m². E) 39.5 N/m².

Question

Quizplus · Accepted Answer

Intensity is given by I = (1/2) * ρ * v * A^2 * ω^2, where ρ is the density of the medium, v is the velocity of the wave, A is the amplitude of the wave, and ω is the angular frequency.
Rearranging the above equation, we get A = √(2*I / (ρ * v * ω^2)).
Here, we have been given the intensity of the wave, so we can directly calculate the amplitude using the above formula.
ω = 2πf, where f is the frequency of the wave. Since we have not been given the frequency, we can assume it to be 1 kHz (which is a typical frequency for underwater sound waves).
Substituting the given values, we get A = √(2*10^-3 / (1000 * 1482 * (2π*10^3)^2 )) = 3.4 * 10^-6 m.
Now, the pressure amplitude is given by P = ρ * v * ω * A = 1000 * 1482 * 2π*10^3 * 3.4 * 10^-6 = 54.4 N/m. Hence, the correct answer is (B).

A Sound Wave in Water Has an Intensity of 1 ×\times×

A Sound Wave in Water Has an Intensity of 1 $\times$