Answer:
[tex]3.4\cdot 10^{-4} kg/m[/tex]
Explanation:
The order of the harmonics for standing waves in a string is equal to the number of nodes minus 1, so
n = 5 - 1 = 4
In this case, the frequency of the 4th-harmonic is
[tex]f_4=1.5 kHz = 1500 Hz[/tex]
We also know the relationship between the frequency of the nth-harmonic and the fundamental frequency:
[tex]f_4 = 4 f_1[/tex]
so we find the fundamental frequency:
[tex]f_1 = \frac{f_4}{4}=\frac{1500 Hz}{4}=375 Hz[/tex]
The fundamental frequency is given by
[tex]f_1 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}[/tex]
where
L = 1.2 m is the length of the string
T = 276 N is the tension in the string
[tex]\mu[/tex] is the linear density
Solving the equation for [tex]\mu[/tex], we find
[tex]\mu = \frac{T}{4L^2 f_1^2}=\frac{276 N}{4(1.2 m)^2(375 Hz)^2}=3.4\cdot 10^{-4} kg/m[/tex]
