# Is there no way to create an arbitrary wave on a string fixed at two ends?

My question concern standing waves on a string with 2 fixed end. As there is one wave created, it will be reflected when it reaches one end and create another identical wave with opposite direction standing wave on the string. 2 fixed end is 2 nodes so the wave length must be $2L/n$ for L to be the length of the string.

As the wave speed is fixed by tension and linear density value and so the frequency must be in harmonic with wave length so any wave created on that string must meet the required wave length and frequency. I want to know if it is really true there is no possible way to create any wave whose frequency and wavelength are different from requirement?

For string fixed on 1 end, is it possible to create an arbitrary wave whose frequency don't meet above requirement. For such 2 waves that's different in wave length and amplitude, can they create a standing wave?

• You say something which is confuse. "As there is one wave created, it will be reflected when it read one end". I assume that you meant "when it reached one end". Well, a standing wave is not a running wave, it is as its name says, "standing". – Sofia Dec 22 '14 at 21:18
• It's not possible to get a reflection from the loose end of the string, so standing waves can only be generated on strings that are fixed on both ends. – David White Feb 18 '19 at 5:32