The equation of a stationary wave in a metal rod is given by y = 0.002 sin π x 3 sin 1 000 t , where x is in cm and t is in second. The maximum tensile stress at a point x = 1 cm is n π 3 × 1 0 8 dyne cm - 2 . What is the value of n ? [Young's modulus of the material of rod is = 8 × 1 0 11 dyne cm - 2 ]

Step-by-step solution

y = 0.002   sin π x 3   sin 1 000 t d y d x = 0.002 π 3   cos π x 3   sin 1 000 t ∵ Tensile stress = Y d y d x The maximum value of the stress at x = 1   c m = Y × 0.002 π 3   cos π 3 = 8 × 1 0 11 × 0.002 × π 3   cos π 3 = 8 π 3 × 1 0 8   dyne   cm - 2 ⇒ n = 8