A standing wave is formed on a string of a given tension, T, linear density, μ, and length, L. If the tension in the string is multiplied by two (T' = 2T) while maintaining the same frequency (f' = f) of the standing wave and the same linear density (μ' = μ) and length of the string (L' = L), then the new number of loops, n', on this string is equal to the old number of loops, n, multiplied by a factor of:
1/4
2
ā2
1/ā2
1/2
The wave functions for two waves traveling on a string are described by:
yā(x,t) = A sin (Ļx - 40Ļt) and yā(x,t) = A sin (Ļx + 40Ļt)
where, y and x are in meters, and t is in seconds. An element of the string oscillating vertically with amplitude A would be located at:
x = (1/18) m
x = (1/12) m
x = (1/15) m
x = (1/6) m