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RUDIKE [14]
3 years ago
13

As it travels through a crystal, a light wave is described by the function E(x,t)=Acos[(1.57×107)x−(2.93×1015)t]. In this expres

sion, x is measured in meters and t is measured in seconds.
Part A
What is the speed of the light wave?
Express your answer to three significant figures and include appropriate units.
Physics
1 answer:
Drupady [299]3 years ago
7 0

Answer:

Speed, v=1.86\times 10^8\ m/s

Explanation:

It is given that,

A light wave is described by the following function as :

E(x,t)=A\ cos[(1.57\times 10^7)x-(2.93\times 10^{15})t].....(1)

The general equation of wave is given by :

E=Acos(kx-\omega t)........(2)

On comparing equation (1) and (2)

k=(1.57\times 10^7)

\dfrac{2\pi}{\lambda}=(1.57\times 10^7)

\lambda=\dfrac{2\pi}{(1.57\times 10^7)}

Wavelength, \lambda=4.002\times 10^{-7}\ m

\omega=(2.93\times 10^{15})

\dfrac{2\pi}{T}=(2.93\times 10^{15})

\dfrac{1}{T}=\dfrac{(2.93\times 10^{15})}{2\pi}

Frequency, f=4.66\times 10^{14}\ Hz

Let v is the speed of the light wave. It is given by :

v=f\times \lambda

v=4.66\times 10^{14}\ Hz\times 4.002\times 10^{-7}\ m

v=1.86\times 10^8\ m/s

So, the speed of the light wave is 1.86\times 10^8\ m/s. Hence, this is the required solution.

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The change in potential energy when the block falls to ground is -480J.

The maximum change in kinetic energy of the ball is 480 J.

The initial kinetic energy of the ball is 0 J.

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<h3>Change in potential energy when the block falls to ground</h3>

ΔP.E = -mgh

ΔP.E = -Wh

ΔP.E = - 40 x 12

ΔP.E = -480 J

<h3>Maximum change in kinetic energy of the ball</h3>

ΔK.E = - ΔP.E

ΔK.E = - (-480 J)

ΔK.E = 480 J

<h3>Initial kinetic energy of the ball</h3>

K.Ei = 0.5mv²

where;

  • v is zero since it is initially at rest

K.Ei = 0.5m(0) = 0

<h3>Final kinetic energy</h3>

K.Ef =  0.5mv²

K.Ef = 0.5(0.0091)(5.7)²

K.Ef = 0.148 J

<h3>Initial potential energy of the ball</h3>

P.Ei = mghi

P.Ei = 0.0091 x 9.8 x 2.1

P.Ei = 0.187 J

<h3>Final potential energy</h3>

P.Ef = mghf

P.Ef = 0.0091 x 9.8 x 0

P.Ef = 0

<h3>Work done by the air resistance</h3>

W = ΔE

W = P.E - K.E

W = 0.187 J - 0.148 J

W = 0.039 J

Learn more about potential energy here: brainly.com/question/1242059

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