Answer:
0.8067 m
69.696 N
Explanation:
m = Mode = 3
M = Mass of string = 4 g
f = Frequency = 180 Hz
l = Length of string = 121 cm
Length of the string is given by
[tex]l=m\dfrac{\lambda}{2}\\\Rightarrow \lambda=2\dfrac{l}{m}\\\Rightarrow \lambda=2\times \dfrac{1.21}{3}\\\Rightarrow \lambda=0.8067\ m[/tex]
The wavelength is 0.8067 m
Linear density is given by
[tex]\mu=\dfrac{M}{l}\\\Rightarrow \mu=\dfrac{4\times 10^{-3}}{1.21}[/tex]
Speed of the wave
[tex]v=f\lambda\\\Rightarrow v=180\times 2\times \dfrac{1.21}{3}\\\Rightarrow v=145.2\ m/s[/tex]
Speed of wave is given by
[tex]v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow T=\mu v^2\\\Rightarrow T=\dfrac{4\times 10^{-3}}{1.21}\times 145.2^2\\\Rightarrow T=69.696\ N[/tex]
Tension is given by 69.696 N
