Angular Frequency of Waves - Optics and Modern Physics - Solved Past Paper, Exams of Physics

Download Angular Frequency of Waves - Optics and Modern Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! 2. A youngster in a boat on a lake watches waves that seem to be an endless succession of identical crests passing with a half-second interval between each. Each disturbance takes 1.5 s to sweep along the the length of the 4.5 m long boat and are 30 cm from top to bottom. a) What is the wave speed? The waves travel the 4.5 m length of the boat in 1.5 s, so the speed is v = 4.5 1.5 = 3 m/s b) What are the frequency and angular frequency of the waves? The period is 0.5 s, which makes the frequency ν = 1 0.5 = 2 Hz Then we can get the angular frequency by ω = 2πν = 2π(2) = 4π = 12.57 rad/s c) Compute the wavelength and propagation constant of the waves. Since v = λν, we have λ = 3 2 = 1.5 m Then k = 2π λ = 2π 1.5 = 4.19 m−1 d) Write down a wave function describing these waves, taking the positive x-axis to be in the direction of propagation. The general form of the wave equation solution is ψ(x, t) = A cos(kx− ωt) Putting in the values from above, and recognizing that the amplitude is one-half of the wave height (from crest to trough), we get ψ(x, t) = 0.15 cos(4.19x− 12.57t) It would be acceptable to have used sin rather than cos.