Question

From the mathematical functions (with x is in metres, t in seconds), select those which correspond to each of the five motions below . For example, if functions A and G satisfy motion 1, function C satisfies motion 2 and none of the functions satisfies motions 3, 4 and 5, enter AGCNNN. (Note that the answers for each motion must be in alphabetical order.)

A) y(x,t) = 0.2 sin(3x−9t)

B) y(x,t) = 0.8 cos(2πx−6πt+π/2)

C) y(x,t) = 0.2 cos(3x)sin(2πt/3)

D) y(x,t) = 0.4 cos(x)sin(t/3)

E) y(x,t) = 0.2 sin(2πx)sin(6πt)

F) y(x,t) = 0.4/(2+(2x−6t)²)

G) y(x,t) = 0.4 sin(2x)cos(6πt)−0.8 sin(x)cos(x)cos(6πt)

H) y(x,t) = 0.2/(1+(x−3t)²) - 0.2/(1+(x+3t)²)

N) none of the above

1) A harmonic wave or wave pulse travelling in the positive x direction at 3 m/s.

2) A motion in which the medium has a wavenumber of 3 m^-1.

3) A motion in which the medium at x = 0 m is fixed, i.e., it is unable to move.

4) A motion in which the movement of the medium corresponds to a wavelength of 1 m.

5) A harmonic travelling wave with a period of 3 seconds.

Answer 1

A B F