The length of a taut string that has a period of one second depends on various factors, such as the tension in the string and the properties of the medium through which the wave propagates.
In the context of simple harmonic motion, the period (T) of a string's vibration is related to its length (L) and the wave speed (v) through the equation:
T = 2L/v
Assuming that the wave speed remains constant, if the period is one second (T = 1 s), then we can rearrange the equation to solve for the length of the string (L):
L = v/2
As you can see, the length of the string is directly proportional to the wave speed. The specific value of the length would depend on the medium and the conditions of the system in which the string is vibrating.