The equation of a wave is represented by :- y = 1 0 − 4 sin ( 100 t − 10 x ) m , where x and y are in meter and t in second; then the velocity of wave will be:-

Question

The equation of a wave is represented by :- y = 1 0 − 4 sin ( 100 t − 10 x ​ ) m , where x and y are in meter and t in second; then the velocity of wave will be:-

TestHub · Accepted Answer

The standard wave equation is y = A sin ( k x − ω t ) . Comparing with y = 1 0 − 4 sin ( 100 t − 10 x ​ ) , we rewrite it as y = 1 0 − 4 sin ( − 10 x ​ + 100 t ) = 1 0 − 4 sin ( 10 x ​ − 100 t ) . Thus, k = 10 1 ​ and ω = 100 . Wave velocity v = k ω ​ = 1/10 100 ​ = 1000 m/s .

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