The equation of a longitudinal stationary wave in a metal rod is given by, `y = 0.002 sin "(pix)/(3) sin 1000pit`, where `x` & `y` are in `cm` and `t` is in seconds. If maximum change in pressure (the maximum tensile stress) at the point `x = 2 cm` is `(1)/(n) xx 10^(-3) "dyne"//"cm"^(2)`, Find `n`. Given young's modulus of the material is `(3)/(8pi) "dynes"//"cm"^(2)`.

Answer

8

Explanation

Strain for longitudinal wave `= (dy)/(dx)`
Stress `= Y` strain `= Y (dy)/(dx)`
for max stress , `(dy)/(dx)` should be max
`y = 0.002 sin "(pix)/(3)sin1000pil`
`(dy)/(dx) = 0.002 (pi)/(3) cos "(pix)/(3) sin 1000pit`
`x = 2, "max" (dy)/(dx) = 0.002 (pi)/(3) cos "(pix)/(3) sin 1000pit`
`x = 2 , "max" (dy)/(dx) = 0.002 (pi)/(x) cos"(pi2)/(3) = -0.002 (pi)/(3) xx (1)/(2)`
stress `= (3)/(8pi) (-0.001 (pi)/(3)) = (0.001)/(8) = (1)/(8) xx 10^(-3) "dyne"//cm^(2)`