Physics
Physics
Problem
A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm, respectively. (a) What is the minimum possible length of the string? (b) If the tension is 10 N and the linear mass density is 4 g/m, what is the fundamental frequency?Intuitive explanation
The key insight is that standing wave modes are numbered by how many half-wavelengths fit in the string's fixed length . For mode , the distance between adjacent nodes is , so you can write two equations relating the string length to consecutive modes. Since stays the same, you can eliminate it and solve for which modes you're observing, then find the actual string length.
Intuitive explanation
The key insight is that standing wave modes are numbered by how many half-wavelengths fit in the string's fixed length . For mode , the distance between adjacent nodes is , so you can write two equations relating the string length to consecutive modes. Since stays the same, you can eliminate it and solve for which modes you're observing, then find the actual string length.