The equation of a travelling wave is y = 5.0 sin 100 (-0.15x + 300t). Calculate (i) the amplitude of the vibrating particle, (ii) wave velocity, (ii) wave length, (iv) frequency and (v)
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A: The expression for the wave function of the wave is, ψ(x, t)=3.5 cos(1.5x- 8.6t+0.46)…
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- #4A distance of 3.30 meters lies between two successive maxima of a transverse wave. Five wave crests pass a stationary observer every 16.7 seconds. (a) Compute the wave's frequency (in Hz). Hz (b) With what speed (in m/s) does the wave travel? m/sA water wave traveling in a straight line on a lake is described by the equation y(x,t)=(2.75cm) cos((0.410rad/cm)x+(6.20rad/s)t) where y is the displacement perpendicular to the undisturbed surface of the lake. (a) How much time does it take for one complete wave pattern to go past a person fishing in a boat at anchor, and what horizontal distance does the wave crest travel in that time? (b) What is the wave number and the number of waves per second that pass the fisher? (c) How fast does a wave crest travel past the fisher, and what is the maximum speed of the cork floater as the wave causes it to bob up and down?
- A sinusoidal wave train is described by y = 25 sin [2π (6x + 5t)] where x and y aremeasured in centimeters (a) What is the magnitude of the maximum transversvelocity and acceleration of the wave? (b) Determine the wavelength and the periodof the wave.A string oscillates according to the equation y = (0.550 cm) sin[(17/5.0 cm-4)x] cos[(25.6 T s-)t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 2.21 cm when t = 1.23 s?A wave in a string obeys the equation y(x,t) = (5.0cm) sin [(13.8 rad/m)x + (2070 rad/s)t + 2.19rad]. Find the velocity of the wave propagation
- Two identical traveling waves, moving in the same direction, are out of phase by z/3.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves? (Give the answer as the ratio of the total amplitude to the common amplitude.) Number i Units(a) What is the speed of the wave (b) What is the displacement of a particle at λ/2. (c) What is the maximum displacement of the wave? y = 2.1sin( 397t +9.23x)A wave is modeled with the function y(x, t) = (0.25 m)cos(0.30 m−1 x − 0.90 s−1 t + π/3). Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) phase shift, (f) wavelength, and (g) period of the wave.
- 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 string oscillates according to the equation y' = (0.752 cm) sin[(7/5.0 cm-1)x] cos[(29.6 t s )t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.74 cm when t = 1.17 s? (a) Number Units (b) Number Units (c) Number Units (d) Number i UnitsA 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.