QualityFactorBandwidth is a handy toolkit for quick wave and signal math. Find angular frequency to see how fast something cycles in radians per second. Turn frequency into period, and compare two tones with beat frequency. Estimate refractive index from wave speed to see how much light slows down. Convert light frequency to photon energy for labs and sensors. Check a resonator’s quality factor from its bandwidth for sharpness. Measure spacing between nodes in standing waves on strings or air columns. Adjust speed for temperature, swap between frequency–wavelength–speed, and handle 1-D Doppler shift—even at high speeds.