Question

A 85.0 cm wire of mass 9.40 g is tied at both ends and adjusted to a tension of 39.0 N . When it is vibrating in its second overtone, find the frequency at which it is vibrating. When it is vibrating in its second overtone, find the frequency of the sound waves it is producing. When it is vibrating in its second overtone, find the wavelength of the sound waves it is producing.

Answer 1

frequency = 104.80 Hz

wavelength = 0.567 m

frequency = 104.80 Hz

wavelength = 3.27 m

Step-by-step explanation:

given data

mass m = 9.4 g = 9.4 ×
`10^(-3)` m

length L = 85 cm = 0.85 m

tension T = 39 N

to find out

frequency and wavelength

solution

first we find frequency for second overtone

f = 3 /2L × √(T/μ) .............1

put here all value and

here μ = m/L = 9.4 ×
`10^(-3)` / 0.85 = 1.10588 ×
`10^(-2)` kg/m

f = 3 /2(0.85) × √(39/1.10588 ×
`10^(-2)`)

f = 104.80 Hz

and

wavelength is 2L/3

wavelength = 2(0.85) / 3

wavelength = 0.567 m

and

frequency = 104.80 Hz

and

wavelength by speed of sound i.e 343 m/s

wavelength = speed / f

wavelength = 343 / 104.80

wavelength = 3.27 m