Physics
Physics
Problem
Strings X and Y have both ends fixed. The speed of transverse waves in X is double that in Y, and the length of X is half that of Y. Determine the ratio of the frequency of the first harmonic in X to that in Y.Intuitive explanation
The key is recognizing that for a string with fixed ends, the fundamental frequency depends on both wave speed and length: . Since string X has twice the wave speed but half the length of string Y, both factors work in X's favor—the numerator doubles while the denominator halves. This means you're looking at how speed and geometry combine to determine the pitch of each string's lowest mode.
Intuitive explanation
The key is recognizing that for a string with fixed ends, the fundamental frequency depends on both wave speed and length: . Since string X has twice the wave speed but half the length of string Y, both factors work in X's favor—the numerator doubles while the denominator halves. This means you're looking at how speed and geometry combine to determine the pitch of each string's lowest mode.