Answer :
The minimum possible length of a string fixed at both ends with given standing wave modes is 144 cm(Option A). This is determined by calculating the least common multiple of the wavelengths corresponding to the given node distances.
Standing waves on a string fixed at both ends have nodes at both ends. The distance between consecutive nodes is half the wavelength (2). Given the distances between adjacent nodes are 18 cm and 16 cm:
- For the first mode, the wavelength (1) is twice the distance between nodes:
1 = 2 x 18 cm = 36 cm. - For the second mode, the wavelength (2) is twice the distance between nodes:
2 = 2 x 16 cm = 32 cm.
The length L of the string must be such that it fits an integer number of half-wavelengths for both 36 cm and 32 cm. We find the smallest common multiple:
- LCM of 36 cm and 32 cm = 144 cm.
Thus, the minimum possible length of the string is 144 cm, so the correct answer is A.
