Standing waves are produced by the superposition of two waves y, = 5 sin (3tt – 2x) y2 = 5 sin (3t + 27x) and where y and x are in cm and t in second. Find the amplitude of the particle at x = 2 cm.

Sinusoidal water waves are generated in a large ripple tank. The waves travel at 24.7 cm/s and their adjacent crests are 8.19 cm apart. What is the time required for one complete oscillation? Express your answer in seconds, to at least two digits after the decimal point.

A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 3.2E-05 m. The motion produces a sound wave that travels at a velocity of v = 336 m/s with a frequency of f = 120 Hz. Take the density of air as ρa = 1.20 kg/m3. Calculate the displacement of the air molecules using an function for the traveling sound wave in terms of time and position at time t = 0.001 s and displacement x = 1.0 m.  Write an expression for the maximum pressure exerted by the sound wave ΔPmax in terms of the air density ρa, the sound velocity v, the angular frequency ω, and the maximum displacement smax. The sound wave is directly incident on a sheet of paper of surface area A = 0.013 m2. Calculate the maximum force Fmax, in newtons, exerted on this sheet.

A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 3.2E-05 m. The motion produces a sound wave that travels at a velocity of v = 336 m/s with a frequency of f = 120 Hz. Take the density of air as ρa = 1.20 kg/m3. Calculate the wavelength λ of the sound wave, in meters.  Calculate the wavenumber k of the sound, in radians per meter.  Calculate the angular frequency of the sound ω, in radians per second.

Harmonic, sinusiodal wave propagates through a string with speed v and frequency f. At a given instant of time, two points on the string have a phase difference of π/8 rad. Calculate the distance between those two point

Problem 2Given: A wave of 0.3 m wave height and period 1.3 seconds is generated in a wave tank. The wave tank is 90 m. long, 3 m wide, and 3 m deep and filled with fresh water to a depth of 1.5 m. The density of water is 997 kg/m3.Evaluate the water particle velocity and acceleration at the crest of the wave at still water level (SWL).