A generator at one end of a very long string creates a wave given by \[ y=(6.0 \mathrm{~cm}) \co...
0A generator at one end of a very long string creates a wave given by
\[
y=(6.0 \mathrm{~cm}) \cos \frac{\pi}{2}\left[\left(2.00 \mathrm{~m}^{-1}\right) x+\left(6.00 \mathrm{~s}^{-1}\right) t\right],
\]
and a generator at the other end creates the wave
\[
y=(6.0 \mathrm{~cm}) \cos \frac{\pi}{2}\left[\left(2.00 \mathrm{~m}^{-1}\right) x-\left(6.00 \mathrm{~s}^{-1}\right) t\right] .
\]
Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave. For \( x \geq 0 \), what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of \( x \) ? For \( x \geq 0 \), what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value of \( x \) ?
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