Question

5) A string with mass density μ and tension T is fixed at the points z=0 and z-L, and supports standing waves of the form f (z, t) = A sin kz coswt. Since these standing waves are produced by counterpropagating travelling waves (due to all of the multiple reflections), the relationship ω-ku still applies, where u is the velocity of the travelling waves. a) In terms of L, what are the allowed, discrete values of the wavenumber kn which satisfy f(0,t)-0 and f(L, t)-0 for all time? Hint: Recall that sin nT 0, where n is an integer b) Given L-1m, T-300N and p 8g/m, what are the three lowest standing-wave frequencies, in Hz, at which the string could vibrate?

Answer 1

standing waves are formed due to superposition of two progreespro waves travelling in opposite direction such that at the fixed ends displacement of wave is minimum known as Node. Distance between suscessive nodes is half the wavelength of wave.