Question

Two waves that set up a standing wave in a long string are given by the wave functions $$y_{1}=A \sin (k x-\omega t+\phi) \quad$ and $\quad y_{2}=A \sin (k x+\omega t)$$ Show (a) that the addition of the arbitrary phase constant $\phi$ changes only the position of the nodes and, in particular, (b) that the distance between nodes is still one half the wavelength.

          Two waves that set up a standing wave in a long string are given by the wave functions
$$y_{1}=A \sin (k x-\omega t+\phi) \quad$ and $\quad y_{2}=A \sin (k x+\omega t)$$
Show (a) that the addition of the arbitrary phase constant $\phi$ changes only the position of the nodes and, in particular, (b) that the distance between nodes is still one half the wavelength.

Added by F-Tima R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Pritesh Ranjan

01/12/2022

Step 1

Step 1: Combine the two wave functions to form a standing wave: $$y = A \sin (kx - \omega t + \phi) + A \sin (kx + \omega t)$$ Show more…

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Two waves that set up a standing wave in a long string are given by the wave functions $$y_{1}=A \sin (k x-\omega t+\phi) \quad$ and $\quad y_{2}=A \sin (k x+\omega t)$$ Show (a) that the addition of the arbitrary phase constant $\phi$ changes only the position of the nodes and, in particular, (b) that the distance between nodes is still one half the wavelength.