Question

Based on reading in the textbook, are standing wave modes directly determined by matching frequency restriction or by matching wavelength restrictions? How do you justify your position? What might be the utility of describing standing waves in terms of the other wave property? That is, if you say wavelength restrictions are primary, why bother describing standing waves in terms of frequency, or vice versa if you claim frequency restrictions are primary.

Answer 1

The reason is simple as the these two quantities viz frequency and wavelength are fundamental and do not change with change in external physical conditions. Also the frequency of a wave is directly its energy up to multiplication of Planck's constant. So these nodes and antinodes of standing waves which represent the energy density should be in terms of frequency or wavelength ( provided speed of wave remains constant). Suppose we utilize speed or some other quantity to specify standing wave than it may alter with change in any physical conditions like temperature pressure etc.