The functions sin θ and sin 2θ are both periodic trigonometric functions, but they differ significantly in frequency and behavior. Sin θ completes one full oscillation over an interval of 2π, while sin 2θ completes two full oscillations in the same interval, meaning it has double the frequency. This makes sin 2θ oscillate faster, with more peaks and troughs compared to sin θ. Additionally, while both functions have the same amplitude and range—from –1 to 1—their zero crossings and turning points

Ch. 16 Introduction to Oscillatory Motion and Waves - College Physics 2e | OpenStax