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

Answer:

Explanation:

For third normal mode of vibration

l = $\frac{3\lambda}{2}$  , λ is wavelength , l is length of string .

.4 = $\frac{3\lambda}{2}$

λ = .267 m

velocity = $\sqrt{\frac{T}{m} }$

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 = $\sqrt{\frac{80}{.00125} }$

= 253 m /s

frequency

= velocity / λ

= 253 / .267

= 947.5 Hz .