Answer:
The beat frequency is 6.378 Hz.
Explanation:
Given that,
Length of wire = 10000 m
Weight = 81.34 N
Distance = 0.660 m
Tension = 52 N
Frequency = 196 Hz
We need to calculate the mass of the wire
Using formula of weight
[tex]W= mg[/tex]
[tex]m = \dfrac{W}{g}[/tex]
Put the value into the formula
[tex]m=\dfrac{81.34}{9.8}[/tex]
[tex]m=8.3\ kg[/tex]
The mass per unit length of the wire
[tex]m_{l}=\dfrac{m}{l}[/tex]
Put the value into the formula
[tex]m_{l}=\dfrac{8.3}{10000}[/tex]
[tex]m_{l}=8.3\times10^{-4}\ kg/m[/tex]
We need to calculate the frequency in the wire
Using formula of frequency
[tex]f_{w}=\dfrac{1}{2l}\sqrt{\dfrac{T}{m_{l}}}[/tex]
Put the value into the formula
[tex]f_{w}=\dfrac{1}{2\times0.660 }\sqrt{\dfrac{52}{8.3\times10^{-4}}}[/tex]
[tex]f_{w}=189.62\ Hz[/tex]
We need to calculate the beat frequency
Using formula of beat frequency
[tex]f_{b}=f_{in}-f_{w}[/tex]
Put the value into the formula
[tex]f_{b}=196-189.622[/tex]
[tex]f_{b}=6.378\ Hz[/tex]
Hence, The beat frequency is 6.378 Hz.
