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Density of modes. The essentials of calculating the number of modes of vibration of waves confined...

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Physics

Density of modes. The essentials of calculating the number ofmodes of vibration of waves confined 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 fixed 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

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