Density of modes. The essentials of calculating the number ofmodes of vibration of waves conï¬ned to a cavity may be understoodby considering a one-dimensional example. (a) Calculate the numberof modes (standing waves of different wavelength) with wavelengthsbetween 2.0 cm and 2.1 cm that can exist on a string with ï¬xed endsthat is 2 m long.
(b) Calculate, in analogy to our three
dimensional calculation, the number of modes per unit wavelengthper unit length, .
(c) Show that in general the number of modes per unit wavelengthper unit length for a string of length L is given
