Question

A 100 cm wire of mass 9.40 g is tied at both ends and adjusted to a tension of 39.0 N

A) When it is vibrating in its second overtone, find the frequency at which it is vibrating.

B) When it is vibrating in its second overtone, find the wavelength at which it is vibrating.

C) When it is vibrating in its second overtone, find the frequency of the sound waves it is producing.

D) When it is vibrating in its second overtone, find the wavelength of the sound waves it is producing.

Answer 1

L = length of wire = 100 cm = 1 m

m = mass = 9.40 g = 9.40 x 10^-3 kg

= mass per unit length = 9.40 x 10^-3 kg/m

T = tension in the wire = 39 N

A)

for second overtone :

f = (3/2L) sqrt(T/)

f = (3/(2 x 1)) sqrt(39/(9.40 x 10^-3))

f = 96.62 Hz

B)

wavelength is given as ::

= 2L/3 = 2 (1) /3 = 0.67 m

C)

f = 96.62 Hz

D)

speed of sound wave = 343 m/s

wavelength = speed /f = 343 / 96.62 = 3.55 m