Two travelling waves superpose to produce a standing wave described by y = 1.0 mm * cos[(1.57 cm⁻¹) x] * sin[(78.5 s⁻¹) t]. In the region x 0, the node closest to the origin is located at x equal to

Question

Two travelling waves superpose to produce a standing wave described by y = 1.0 mm * cos[(1.57 cm⁻¹) x] * sin[(78.5 s⁻¹) t]. In the region x > 0, the node closest to the origin is located at x equal to

Accepted Answer

1 cm. For a standing wave y = A*cos(kx)*sin(wt), nodes occur where cos(kx) = 0, i.e., kx = (2n-1)*pi/2 for n = 1, 2,... The smallest positive x is at n=1: x = pi/(2k).

Two travelling waves superpose to produce a standing wave described by y = 1.0 mm * cos[(1.57 cm⁻¹) x] * sin[(78.5 s⁻¹) t]. In the region x > 0, the node closest to the origin is located at x equal to

Solution

Related JEE Advanced Physics questions