Formation of standing wave through reflection of a sinusoidal wave at a fixed end.

Wavelength = 2.

> with(plots):
animate(sin(Pi*(t-x))*Heaviside(t-x)-sin(Pi*(t+x))*Heaviside(t+x),x=-6..0,t=-5.99..12,frames=200,numpoints=200,color=red);

[Maple Plot]

Standing wave in a string (both ends clamped).

The lowest order fundamentral mode. Lambda = 2*L. (L = string length) Frequency f_1 = c_w/(2L).

> with(plots):
animate(sin(Pi*x)*sin(t),x=0..1,t=0..2*Pi,frames=60,color=red);

[Maple Plot]

Second harmonic mode. Lambda = L. Frequency 2*f_1.

> animate(sin(2*Pi*x)*sin(2*t),x=0..1,t=0..2*Pi,frames=60,color=red);

[Maple Plot]

Third harmonic mode. Lambda = (2/3)L. Frequency 3*f_1.

> animate(sin(3*Pi*x)*sin(3*t),x=0..1,t=0..2*Pi,frames=60,color=red);

[Maple Plot]

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