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Two waves are generated on a string of length 3.0 m to produce a three-loop standing wave with an amplitude of 1.0 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x, t) # ym sin(kx " vt). In the equation for the other wave, what are (a) ym, (b) k, (c) v, and (d) the sign in front of v?

Respuesta :

Answer:

Part a)

[tex]y_m = 1 cm[/tex]

Part b)

[tex]k = \pi rad/m[/tex]

Part c)

v = 100 m/s

Part d)

since wave is moving in +x direction

so here the sign must be negative

so complete wave equation is

[tex]y = (1 cm) sin(\pi(x - 100t))[/tex]

Explanation:

As we know that the wave equation is given as

[tex]y = y_m sin(k(x " vt))[/tex]

here we know that

[tex]y_m [/tex] = maximum displacement of the particle

Part a)

maximum displacement = amplitude

so here we know that

[tex]y_m = 1 cm[/tex]

Part b)

k = [tex]\frac{2\pi}{\lambda}[/tex]

here we know that length of the string is 3 m

it consist of 3 loops

so we will have

[tex]3 \frac{\lambda}{2} = 3 m[/tex]

[tex]\lambda = 2 m[/tex]

so we have

[tex]k = \frac{2\pi}{2}[/tex]

[tex]k = \pi rad/m[/tex]

Part c)

v = wave speed

v = 100 m/s

Part d)

since wave is moving in +x direction

so here the sign must be negative

so complete wave equation is

[tex]y = (1 cm) sin(\pi(x - 100t))[/tex]

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