A stationary wave on a string is represented by the equation y = 12 ( x 6 ) (50 t) , where x and y are in cm and t is in seconds. The minimum positive value of x at which a particle of the string oscillates with an amplitude of 6 cm is ________.

Step-by-step solution

The amplitude of a particle at position x in the stationary wave is given by the magnitude of the spatial part of the wave equation: A(x) = |12 ( x 6 ) | We are given that the amplitude is 6 cm . Therefore, |12 ( x 6 ) | = 6 ( x 6 ) = 1 2 To find the minimum positive value of x , we take the smallest positive angle whose sine is 1 2 : x 6 = 6 x = 1 cm Answer: 1