Answer :

Given:


The equation of the wave y = 2cos[2π(10t-0.0080x+3.5)]


(a) For the wave separated by a distance of 4 m the equation of vibration will be,



or


and the phase



Comparing this equation to the original equation



and the phase



the phase difference therefore



(b) For a separation of 0.5 m, proceeding as above,




and the phase



Comparing this equation to the original equation its phase



the phase difference therefore



(c) The wavelength of the equation can be found by comparing the equation to the general equation for the wave,



we have, k = 0.016π and ω =20π. We know that k is related to the wavelength as



where λ is the wavelength. Therefore for k = 0.016π we have



For a separation of or 0.625 m,




and the phase



Comparing this equation to the original equation its phase



the phase difference therefore



(d) For a separation of or 0.938 m, proceeding as above




and the phase



Comparing this equation to the original equation its phase



the phase difference therefore



(e) At x = 100 cm the equation of the wave becomes,




We know that ω is and time period T are related as



but ω = 20π,



At t = T= 0.1 s the equation of the wave is given by,



and the phase



At t = 5 s the equation of the wave is given by,



and the phase



the phase difference therefore



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