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

Density of modes. The essentials of calculating the number of modes of vibration of waves conﬁned to a cavity may be understood by considering a one-dimensional example. (a) Calculate the number of modes (standing waves of different wavelength) with wavelengths between 2.0 cm and 2.1 cm that can exist on a string with ﬁxed ends that is 2 m long.

(b) Calculate, in analogy to our three

dimensional calculation, the number of modes per unit wavelength per unit length, .

(c) Show that in general the number of modes per unit wavelength per unit length for a string of length L is given

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genius_generous answered 1 year ago

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