Question

Calculate the frequency of the 3rd normal mode of a guitar string of length 40.0cm and mass 0.5g when stretched with a tension of 80N.

Answer 1

Step-by-step explanation:

For third normal mode of vibration

l =
`(3\lambda)/(2)` , λ is wavelength , l is length of string .

.4 =
`(3\lambda)/(2)`

λ = .267 m

velocity =
`\sqrt{(T)/(m) }`

T is tension and m is mass unit length

m = .5 x 10⁻³ / 40 x 10⁻²

= .00125 kg / m

Putting the values

velocity =
`\sqrt{(80)/(.00125) }`

= 253 m /s

frequency

= velocity / λ

= 253 / .267

= 947.5 Hz .