A string oscillates according to the equation y´ = (0.531 cm) sin[(π/4.0 cm-1)x] cos[(37.1 π s-1)t].?
A string oscillates according to the equation y´ = (0.531 cm) sin[(π/4.0 cm^-1)x] cos[(37.1 π s^-1)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 = 2.31 cm when t = 1.49 s? Give your answers in centimeter-based units.
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notice this is a sanding wave. so it can be obtained by two waves traveling in opposite directions with the same frequency. the wavelength of the wave is just the one of the standing wave.
use the following formula
sin(kx-wt) + sin(kx + wt) = 2* sin(kx)cos(wt) where k = 2*π/lambda
so
a) to get the equation of the wave above y = (0.531 cm) * sin.. you need each of the traveling waves tto have an amplitude of 0.531/2 = 0.2655 cm
c) lambda - the wavelength is just calculated by 2*π/lambda = π//4 namely lambda = 0.5 cm
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