Halliday, Resnick & Walker — Waves–I: Problem Problem_96

Ratios. Four sinusoidal waves travel in the positive x direction along the same string. Their frequencies are in the ratio 1:2:3:4, and their amplitudes are in the ratio \(1 : \frac{1}{2} : \frac{1}{3} : \frac{1}{4}\), respectively. When \(t = 0\), at \(x = 0\), the first and third waves are \(180^\circ\) out of phase with the second and fourth. What wave functions satisfy these conditions?