Recall that a wave packet moves with group velocity vg = ∂ω ∂k . for the wave packet above, find vg, evaluated at the central wavenumber k0. if the momentum of a particle is mvg and the kinetic energy is 1 2mv2 g , find the momentum and kinetic energy in terms of k0 and other constants.

Wo audio speakers are placed on a vertical rail. speaker a is placed at head-level while speaker b is place at some variable height, \delta yδy, above speaker a. both speakers receive simultaneous input from a sine-wave generator so the speakers each produce a pure sinusoidal sound wave with a wavelength of 0.531 meters. calculate the lowest height that speaker b can be placed above speaker a to produce a minimum of sound heard by person standing \delta x = 7.86δx=7.86 meters directly in front of speaker a.

An ideal polarizer with its transmission axis rotated 30 degrees to the vertical is placed in a beam of unpolarized light of intensity 10w/m^2. after passing through the polarizer, what is the intensity of the beam? a. 8.7 w/m^2 b. 7.5 w/m^2 c. 5.0 w/m^2 d. 10 w/m^2 e. 2.5 w/m^2

The frequency of the fundamental of the guitar string is 320 hz. at what speed v do waves move along that string?