A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be __________ cm.
Physics · Circular Motion
JEE Mains 8 April 2023 Shift 2 Evening Shift

Question

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be __________ cm.

G1 Physics · Accepted Answer

For a stretched string with unchanged tension and linear mass density, fundamental frequency is f = v/(2L) Therefore, f ∝ 1/L So, f₁L₁ = f₂L₂ Given: f₁ = 120 Hz L₁ = 90 cm f₂ = 180 Hz Therefore, L₂ = (120×90)/180 = 60 cm Final value: 60