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3 years ago

13

a summer thunderstorm has begun! it’s raining. lighting cracks through air. a few seconds later you hear booms of thunder. why d

o you see the lighting before you hear the thunder?

2 answers:

Afina-wow [57]3 years ago

8 0

Lightning comes before sound, other wise said, light travels faster than sound

Hope this helps.

Illusion [34]3 years ago

4 0

Light travels faster than sound

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Answer:

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$y(x,t) = A\cos(kx + \omega t)=(3.3\times 10^{-2})\cos(0.004x + 5.05t)\\$

According to the above equation, k = 0.004 and ω = 5.05.

Using the following identities, we can find the period of the wave.

$\omega = 2\pi f\\ f = 1/ T$

T = 1.25 s.

For the horizontal distance travelled by one period of time, x = λ.

$\lambda = 2\pi / k = 2\pi / 0.004 = 1.57\times 10^3~m$

$y(x = \lambda,t = T) = 0.033\cos(0.004*1.57*\10^3 + 5.05*1.25) = 0.033~m$

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C) The propagation speed of the wave is

$v = \lambda f = 1.57\times 10^3 * 0.8 = 1.256\times 10^3~m/s$

The velocity of the wave is the derivative of the position function.

$v(x,t) = \frac{dy(x,t)}{dt} = -(5.05\times 0.033)\sin(0.004x + 5.05t)$

The maximum velocity is when the derivative of the velocity function is equal to zero.

$\frac{dv_y(x,t)}{dt} = -(5.05)^2(0.033)\cos(0.004*1.57\times 10^3 + 5.05t) = 0$

In order this to be zero, cosine term must be equal to zero.

$0.004*1.57\times 10^3 + 5.05t = 5\pi /2\\t = 0.31~s$

The reason that cosine term is set to be 5π/2 is that time cannot be zero. For π/2 and 3π/2, t<0.

$v(x=\lambda, t = 0.31) = -(5.05\times0.033)\sin(0.004\times 1.57\times 10^3 + 5.05\times 0.31) = -0.166~m/s$

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