Waves & Interference

Periodic Motion and Waves

Period and frequency are reciprocals, $f = 1/T$. A mass on a spring has $T = 2\pi\sqrt{m/k}$ and a pendulum $T = 2\pi\sqrt{L/g}$; neither depends on the amplitude. Every wave obeys $v = f\lambda$: the medium sets the speed, the source sets the frequency.

Interference and Standing Waves

Overlapping waves add. A path difference of a whole number of wavelengths interferes constructively; an odd number of half-wavelengths, destructively. Two close frequencies beat at $|f_1 - f_2|$. A string fixed at both ends, or a pipe open at both ends, supports every harmonic, $f_n = nv/2L$; a pipe closed at one end supports only odd harmonics, $f_n = nv/4L$.

Key Takeaways

• Medium sets speed; source sets frequency.
• Path difference, in wavelengths, decides the interference.
• Closed-end pipes: odd harmonics only.