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Answer :
The minimum possible length of the string is found by calculating the lowest common multiple of the half-wavelengths of consecutive standing wave modes, resulting in a length of 144 cm.The correct option is A 144 cm
The question is about finding the minimum possible length of a string that supports consecutive standing wave modes. When a string is fixed at both ends, standing wave patterns can occur at certain frequencies where the length of the string is an integer multiple of half-wavelengths. If the distances between adjacent nodes are 18 cm and 16 cm, these lengths represent half-wavelengths for consecutive modes (n and n+1).
To find the minimum possible length of the string, we look for the smallest common multiple of these half-wavelengths since the overall length of the string must accommodate an integer number of half-wavelengths for both modes. This common multiple would be:
L = Lowest Common Multiple (9 cm, 8 cm) * 2 = 72 cm * 2 = 144 cm
Therefore, the minimum length of the string is 144 cm, making the correct answer (A) 144 cm.
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