How can I do a standing front/back flip?

Velocity and Frequency of standing waves?

• Standing waves results from interfering waves. As we have when a sting is fixed at one end with an oscillator creating pulses at the other end.  But the incident waves and reflected waves have a specific frequency and wavelength. When the formula for the velocity of a wave is used to find the length of the string , do we use wavelength of the waves creating the standing wave or the standing wave itself? To me it makes sense that it would be the same wavelength.  Also how do we define the frequency of a standing wave. Is it the the number of times per second a particle moves from max displacement to minimum and back to max displacement? Then this would just be the frequency of the incident wave.  I'm a bit confuse here because I see the wavelength of the standing wave itself being used in the velocity formula, but the standing wave has no velocity. It makes sense when the waves along the string is used.

• Answer:

  The frequency of a standing wave is perfectly well defined and has the same value as for the underlying traveling wave: it's f=1/T where the period T is the time for any particle to go through a whole cycle, e.g., from max to min and back again. (If you don't have a single common frequency at every point you don't have a true standing wave, rather it'll be a mix of harmonics.) By contrast, a standing wave really doesn't have a well-defined wavelength of its own. In the simple case where you have a uniform, infinitely flexible wire, the underlying velocity will be constant and the standing wave will look like an integral number of half-periods of a sinusoid (1/2, 1, 1 1/2, 2 etc). If you take one sinusoid's worth then that's the wavelength of the underlying traveling wave, and that's probably the wavelength you're supposed to used in the formula you mention. Just keep in mind that when you go on to consider more complicated situations like non-uniform wires or wire with intrinsic stiffness, and standing waves in organ pipes and woodwind and brass instruments, that there may not be a constant wave velocity from one end of the medium to the other, and thus not a constant wavelength. As a result, the standing wave may not be a perfect sinusoid. (The reason I make a fuss of this is that the case of standing waves is just a particularly simple special case of the much bigger and more general phenomenon of normal modes, a.k.a., eigenmodes, where it's not usually helpful to think of an underlying wave or a wavelength for it.)