Question

A 62.00-cm guitar string under a tension of 70.000 N has a mass per unit length of 0.10000 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 18,000 Hz? (Enter your answer to at least five significant figures.)

Answer 1

17,947.02 Hz

Step-by-step explanation:

length (L) = 62 cm = 0.62 m

tension (T) = 70 N

mass per unit length (μ) = 0.10000 g/cm = 0.010000 kg/m

maximum frequency = 18,000 Hz

f =
`(n)/(2L) x \sqrt{(T)/(μ)}`

f =
`(n)/(2 x 0.62) x \sqrt{(70)/(0.01) }`

f = n x 67.47

18,000 = n x 67.47

n = 266.8≈ 266

the 267th overtone is the highest overtone that can be heard by this person, and its frequency would be 26 x 67.47 = 17,947.02 Hz