A string of linear mass density μ = 0.25 kg/m is stretched between two supports with a uniform tension of 400 N. Find the wavelength λ and frequency ω for the first three harmonics.

In a liquid with a density of 1100 kg/m3, longitudinal waves with a frequency of 370 Hz are found to have a wavelength of 7.50 m. Calculate the bulk modulus of the liquid. Express your answer in pascals.

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.

Consider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then: A. Calculate the period τ and the optical frequency v for green light? B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2). C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.

Find the proportion of energy of a transverse wave that is transmitted across the join between two strings of differing density (ρ) and wave speed (c). Write your answer in terms of the impedances of the two strings (z1 = ρ1c1 and z2 = ρ2c2).

A piano wire with mass 2.60g and length 81.0cm is stretched with a tension of 30.0N . A wave with frequency 110 Hz and amplitude 1.40 mm travels along the wire. (a)Calculate the average power carried by the wave. (b)What happens to the average power if the wave amplitude is halved?

A string of mass 16.6 grams and length 0.74 meters and fixed at the ends is under tension 243 N. What is the vibrational frequency of n= 4 harmonic?

Another Wave Equation With Damping Determine the specific solution to the wave equation with damping ди(х, 1) Ə²u(x,t) ôx² ô²u(x,t) + 4 for 0 < x < n and 0 < t, given also the BCs: u(0,t) initial conditions O and u(n,t) = 0 for 0 < t and the ôu(x,t) u(х,0) : = x and -0

In the figure, a string, tied to a sinusoidal oscillator at Pand running over a support at Q, is stretched by a block of mass m. Separation L 1.3 m, linear density u= 1.1 g/m, and the oscillator frequency f= 120 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. %3D %3D (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m = 1 kg (Give O if the mass cannot set up a standing wave)? %3D Oscillator L- Units (a) Number i Units (b) Number