This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Alright Ridoskynation — let's do this. The given equation for a plane progressive wave is: y = A (2000t - ()/(16)x) This equation is in the standard form y = A ( t - kx), where: • A is the amplitude • is the angular frequency • k is the wave number From the given equation, we can identify: Angular frequency, = 2000 rad/s Wave number, k = ()/(16) rad/m Now, let's calculate the required quantities. Step 1: Calculate the wavelength (). The wave number k is related to the wavelength by the formula k = (2)/(). Rearranging for : = (2)/(k) Substitute the value of k: = (2)/()16 = 2 × (16)/() = 32\, m The wavelength is 32 m. Step 2: Calculate the frequency (f). The angular frequency is related to the frequency f by the formula = 2 f. Rearranging for f: f = ()/(2) Substitute the value of : f = (2000)/(2) f = (1000)/()\, Hz Using ≈ 3.142: f ≈ (1000)/(3.142) ≈ 318.3\, Hz The frequency is 318.3 Hz. Step 3: Calculate the speed (v) of the wave. The speed of the wave v can be calculated using the formula v = ()/(k). Substitute the values of and k: v = (2000)/()16 v = 2000 × (16)/() v = (32000)/()\, m/s Using ≈ 3.142: v ≈ (32000)/(3.142) ≈ 10184.6\, m/s The speed of the wave is 10184.6 m/s. Step 4: Calculate the period (T) of the wave. The period T is the reciprocal of the frequency f: T = (1)/(f) Substitute the exact value of f: T = (1)/(1000) T = ()/(1000)\, s Using ≈ 3.142: T ≈ (3.142)/(1000) ≈ 0.003142\, s The period is 0.003142 s. Send me the next one 📸