String Harmonic Wavelength And Frequency — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
String Harmonic Wavelength and Frequency This set of formulas applies to standing waves (harmonics) formed by transverse vibrations on a string fixed at both ends. The fundamental standing wave equation for fixed ends is y(x, t) = A sin (kx) sin ( t) . Boundary conditions require the wave function to be zero at x=0 and x=L . This leads to the condition kL = n , where n is the harmonic number. The relationship between wave speed, frequency, and wavelength is v = f . Combining these yields the wavelength n = 2L n and the frequency f n = n v 2L . n must be a positive integer (n = 1, 2, 3, ...) The wave must be transverse, and the ends must be fixed. Assuming the fundamental frequency ( n=1 ) is the only frequency present (overlooking higher harmonics). Confusing the wave speed v with the wave frequency f or the wave number k . Using the formula for open ends (where L/n is used instead of 2L/n ).