A

To determine the length of a stretched string fixed at both ends with n nodes, we apply the fundamental concepts of standing waves.
Step 1: In a string fixed at both ends, the distance between two successive nodes is equal to half the wavelength, \( \frac{\lambda}{2} \).
Step 2: With n nodes, there are (n-1) segments of the wave between the nodes. Thus, the total length of the string (L) can be expressed as:
\[ L = (n-1) \cdot \frac{\lambda}{2}
\\ ext{Since the length from one end to the first node is half a wavelength,}
\text{L can also be expressed in terms of n as:}
L = n\cdot \frac{\lambda}{2} \]
Step 3: Therefore, the final formula becomes:
\[ L = \frac{n\lambda}{2} \]
Thus, the length of the string, when it has n nodes, is \( \frac{n\lambda}{2} \). Therefore, the correct answer is option A.