Answer :
Answer:
Tension = 0.034 N
Frequency in two segments = 336 1/s
Explanation:
The frequency of a string is given by
[tex]f=\dfrac{k}{2l}\sqrt{\dfrac{T}{\mu}}[/tex]
k represents the mode of vibration; for the fundamental frequency, k = 1
l is the length of the string in metre
T is the tension of the string in newton
[tex]\mu[/tex] is the linear density or mass per unit length in kg/m; it is a measure of the thickness of the string
Making T the subject of the formula,
[tex]T =(2fl\mu)^2[/tex]
f = 168
l = 86.7 cm = 0.867 m
[tex]\mu = \dfrac{0.55 \text{ g}}{86.7\text{ cm}} = \dfrac{0.00055 \text{ kg}}{0.867\text{ m}} = 6.3\times10^{-4} \text{ kg/m}[/tex]
Then
[tex]T =(2\times168\times0.867\times\dfrac{0.00055}{0.867})^2 = 0.034 \text{ N}[/tex]
When the string vibrates in two segments, it is in the second harmonic. This is simply twice the fundamental frequency.
Hence, f = 2 × 168 = 336 1/s