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3 years ago

9

A string tied between two post is oscillating at 3Hz. A student determines the standing waves have a length of 4 meters. What is

the velocity of the wave?

1 answer:

torisob [31]3 years ago

8 0

Answer:

12 m/s

Explanation:

Standing waves are waves that are formed between two fixed points in space, so they cannot propagate, but they are just oscillations about a fixed points. Examples of standing waves are the waves in a string.

The relationship between wavelength, frequency and speed of a wave is given by the wave equation:

$v=f \lambda$

where

v is the speed of the wave

f is its frequency

$\lambda$ is its wavelength

For the standing wave in this problem we have:

f = 3 Hz is the frequency of the wave

$\lambda=4 m$ is the wavelength

Solving for v, we find the velocity of the wave:

$v=(3)(4)=12 m/s$

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Where $r_{X}=1.2(10)^{6}m$

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For satellite Y, the orbital period $T_{Y}$ is:

$T_{Y}^{2}=\frac{4\pi^{2}}{GM}r_{Y}^{3}$ (5)

Where $r_{Y}=1.9(10)^{5}m$

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<u>For Satellite X:</u>

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$V_{X}=\sqrt{\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(5.972(10)^{24}kg)}{1.2(10)^{6}m}}$

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$V_{Y}=\sqrt{\frac{GM}{r_{Y}}}$ (10)

$V_{Y}=\sqrt{\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(5.972(10)^{24}kg)}{1.9(10)^{5}m}}$

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