Given below are some functions of x and t to represent the displacement the displacement ( transverseor longitudinal ) of an elastic wave. State which
Given below are some functions of x and t to represent the displacement the displacement ( transverseor longitudinal ) of an elastic wave. State which of these represent (i) atravelling wave, (ii) a stationary wave or ( iii) none at all `:`
(a) ` y = 2cos ( 3x ) sin ( 10 t )`
(b) ` y= 2 sqrt(x-vt)`
(c ) `y =3 sin ( 5x - 0.5 t ) + 4 cos ( 5x- 0.5 t ) `
(d) `y cos x sin t+ cos 2x sin 2t `
1 Answers
(a) It represents a stationary wave as harmonic functions of x & t are contained separately in the equation .
(b) It cannot represent any type of wave.
(c ) It represents a progressive `//` travelling harmonic wave.
(d ) This equation is sum of two functions each representing a stationary wave. Therefore it represents superposition of two stationary waves.