A traveling wave on a long string is described by the time-dependent wave function

\[f(x, t)=a \sin (b x-q t),\]

with \(a=6.00 \times 10^{-2} \mathrm{~m}, b=5 \pi \mathrm{m}^{-1}\), and \(q=314 \mathrm{~s}^{-1}\). You want a traveling wave of this frequency and wavelength but with amplitude \(0.0400 \mathrm{~m}\). Write the timedependent wave function for a second traveling wave that could be added to the same string in order to achieve this.