Answer:
145.52137 m/s
1.4 m
0.7 m
60.6339 Hz
121.2678 Hz
Explanation:
T = Tension = 120 N
[tex]\mu[/tex] = Linear density = [tex]\frac{m}{L}[/tex]
m = Mass of wire = 6.8 g
L = Length of wire = 1.2 m
n = Number of loops
Velocity is given by
[tex]v=\sqrt{\frac{T}{\mu}}\\\Rightarrow v=\sqrt{\frac{T}{\frac{m}{L}}}\\\Rightarrow v=\sqrt{\frac{120}{\frac{6.8\times 10^{-3}}{1.2}}}\\\Rightarrow v=145.52137\ m/s[/tex]
The speed of waves on the wire is 145.52137 m/s
Wavelength is given by
[tex]\lambda=\frac{2L}{n}\\\Rightarrow \lambda=\frac{2\times 1.2}{1}\\\Rightarrow \lambda=1.4\ m[/tex]
The wavelength of the waves that produces one-loop standing waves is 1.4 m
[tex]\lambda=\frac{2L}{n}\\\Rightarrow \lambda=\frac{2\times 1.2}{2}\\\Rightarrow \lambda=0.7\ m[/tex]
The wavelength of the waves that produces two-loop standing waves is 0.7 m
Frequency is given by
[tex]f=\frac{nv}{2L}\\\Rightarrow f=\frac{1\times 145.52137}{2\times 1.2}\\\Rightarrow f=60.6339\ Hz[/tex]
The frequency of the waves that produces one-loop standing waves is 60.6339 Hz
[tex]f=\frac{nv}{2L}\\\Rightarrow f=\frac{2\times 145.52137}{2\times 1.2}\\\Rightarrow f=121.2678\ Hz[/tex]
The frequency of the waves that produces two-loop standing waves is 121.2678 Hz
