The displacement y is expressed as a function of x and t in terms of the wave numberk and the angular frequency. Write the equivalent equations in which y is shown as a function…

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asked Dec 2, 2020 101k views

1 Answer

Kyrenia · Answer 1 · 2020-12-09T04:23:00+0000

Step-by-step explanation:

The displacement equation is given by :

(a)
$y=A\ sin(\omega t\pm kx)$

Since,
$\omega=2\pi f$

$\lambda=(2\pi)/(k)$

$y=A\ sin(2\pi f t\pm kx)$

$y=A\ sin((2\pi vt)/(2\pi /k)\pm kx)$

$y=A\ sin(kvt+kx)$

$y=A\ sink(vt+x)$

The above equation is in terms of k and v.

(b)
$y=A\ sin(\omega t\pm kx)$

$y=A\ sin(2\pi (v)/(\lambda)t\pm(2\pi)/(\lambda)x)$

$y=Asin(2\pi)/(\lambda)(vt\pm x)$

(c)
$y=A\ sin(\omega t\pm kx)$

$y=A\ sin(2\pi f t\pm (2\pi)/(\lambda) x)$

$y=A\ sin\ 2\pi (ft\pm (x)/(\lambda))$

(d)
$y=A\ sin(\omega t\pm kx)$

$y=A\ sin(2\pi ft+(2\pi)/(\lambda)x)$

$y=A\ sin(2\pi ft+(2\pi)/(v/f)x)$

$y=A\ sin\ 2\pi f(t+(x)/(v))$

Where

k is the propagation constant

v is the speed of wave

f is the frequency of a wave

$\lambda$ is the wavelength

Hence, this is the required solution.