A transverse wave has a frequency of v = 88.5 Hz and a wavelength of \lambda = 9 m. The wave...
Question:
A transverse wave has a frequency of v = 88.5 Hz and a wavelength of {eq}\lambda {/eq} = 9 m. The wave obtains a maximum displacement of {eq}y_m {/eq} = 1.6 m and propagates in the -x-direction.
(a) Given the form y(x, t) = A sin(B) for the displacement of the wave, input expression for A.
(b) Using the same form y(x, t) input expression for B.
(c) How fast is the wave traveling in m/s?
Waves:
A wave is nothing more than propagation in space and time of disturbance of a physical magnitude. That is, the oscillation of its value with respect to its equilibrium position. The waves can be separated into transverse waves (the direction of propagation is perpendicular to the disturbance of the magnitude that originates the wave) and longitudinal waves (the direction of propagation is in the same direction of the disturbance of the magnitude that originates the wave ). The general equation for a one-dimensional sinusoidal transverse wave traveling to the left is:
{eq}y(x,t)=y_{\max}\sin(kx+\omega t +\varphi ) {/eq}
where {eq}y_{\max} {/eq} is the amplitude of the wave, {eq}\omega {/eq} is the angular velocity, {eq}t {/eq} the time, {eq}k {/eq} the wave vector, {eq}x {/eq} the spatial coordinate, and {eq}\varphi {/eq} is the initial phase.
Answer and Explanation: 1
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View this answer(a) The maximum displacement {eq}y_m {/eq} is equal to the amplitude of wave {eq}A {/eq}, thus:
{eq}\therefore A=\mathrm {1.6\,m} {/eq}
(b) The...
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