Question

10.6. Go back to the original functions but change one of the minus signs to a plus sign (so now f(x,t) = 2.0*sin(x+t) and g(x,t) = 2.0*sin(x-t). The sum u(x,t) is called a standing wave in this case (an example would be the waves on a guitar string). Describe the behavior of u(x,t). How does the period and wavelength of the combined wave compare to the period and wavelength of two components? How is the maximum amplitude of the sum related to the amplitudes of the two components? What can you say about the speed of the sum?

Answer 1

Answer:

The period of the wave does not change looting the value that accompanies the time, the wavelength does not change since it is the constant that accompanies x.

We see that the amplitude is twice the amplitude of the incident waves. Since the wave is stationary the velocity is zero

Explanation:

In this exercise we are given the equation of two traveling waves, it is asked to find the resulting wave

    u = f + g

    u = 2 sin (x + t) + 2 sin (x-t)

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    u = 2 [(sin x cos t + sin t cos x) + (sin x cos t - sin t cos x)]

    u = 2 [2 sin x cos t]

    u = 4 sin x cos t

The period of the wave does not change looting the value that accompanies the time, the wavelength does not change since it is the constant that accompanies x.

We see that the amplitude is twice the amplitude of the incident waves. Since the wave is stationary the velocity is zero