High School

A string fixed at both ends has consecutive standing wave modes where the distances between adjacent nodes are 18 cm and 16 cm, respectively. What is the minimum possible length of the string?

A. 144 cm
B. 152 cm
C. 176 cm
D. 200 cm

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.