The answer is C because <span>this movement is caused by the heat in Earth and creates </span>convection currents. <span>Convection currents in the asthenosphere cause movement of Earth's tectonic plates. </span>
Answer is c that is he particles move perpendicular to the direction of the wave.
Answer:
Max speed = ![\frac{15\, \pi}{4} \,\, \frac{m}{s}](https://tex.z-dn.net/?f=%5Cfrac%7B15%5C%2C%20%5Cpi%7D%7B4%7D%20%5C%2C%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D)
Max acceleration = ![\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}](https://tex.z-dn.net/?f=%5Cfrac%7B15%5C%2C%5Cpi%5E2%7D%7B16%7D%20%5C%2C%5C%2C%5Cfrac%7Bm%7D%7Bs%5E2%7D)
Explanation:
Given the description of period and amplitude, the SHM could be described by:
![f(x)=5\,sin(\frac{\pi}{4}x)](https://tex.z-dn.net/?f=f%28x%29%3D5%5C%2Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7Dx%29)
and its angular velocity can be calculated doing the derivative:
![f(x)=5\, \,sin(\frac{\pi}{4}x)\\f'(x)=5\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)](https://tex.z-dn.net/?f=f%28x%29%3D5%5C%2C%20%5C%2Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7Dx%29%5C%5Cf%27%28x%29%3D5%5C%2C%5Cfrac%7B%5Cpi%7D%7B4%7D%5C%2Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7Dx%29)
And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):
and is given in m/s.
Then the maximum speed is obtained when the cosine function becomes "1", and that gives:
Max speed = ![\frac{15\, \pi}{4} \,\, \frac{m}{s}](https://tex.z-dn.net/?f=%5Cfrac%7B15%5C%2C%20%5Cpi%7D%7B4%7D%20%5C%2C%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D)
The acceleration is found from the derivative of the velocity expression, and therefore given by:
![acceleraton(x)=-15\,\frac{\pi^2}{16}\,sin(\frac{\pi}{4}x)](https://tex.z-dn.net/?f=acceleraton%28x%29%3D-15%5C%2C%5Cfrac%7B%5Cpi%5E2%7D%7B16%7D%5C%2Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7Dx%29)
and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:
Max acceleration = ![\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}](https://tex.z-dn.net/?f=%5Cfrac%7B15%5C%2C%5Cpi%5E2%7D%7B16%7D%20%5C%2C%5C%2C%5Cfrac%7Bm%7D%7Bs%5E2%7D)
Answer:
The wavelength in vacuum is equal to 428.8 nm.
Explanation:
Given that,
The wavelength of light, ![\lambda=284\ nm](https://tex.z-dn.net/?f=%5Clambda%3D284%5C%20nm)
The refractive index of glass, n = 1.51
We need to find the wavelength in vacuum. The relation between wavelength and refractive index is given by :
![n=\dfrac{\lambda_v}{\lambda}\\\\\lambda_v=n\times \lambda\\\\\lambda_v=1.51\times 284\\\\\lambda_v=428.8\ nm](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B%5Clambda_v%7D%7B%5Clambda%7D%5C%5C%5C%5C%5Clambda_v%3Dn%5Ctimes%20%5Clambda%5C%5C%5C%5C%5Clambda_v%3D1.51%5Ctimes%20284%5C%5C%5C%5C%5Clambda_v%3D428.8%5C%20nm)
So, the wavelength in vacuum is equal to 428.8 nm.