Respuesta :
Answer:
The length of the string is 0.266 meters.
Explanation:
It is given that,
Mass of the string, [tex]m=5.5\times 10^{-3}\ kg[/tex]
Tension in the string, T = 230 N
Frequency of wave, f = 160 Hz
Wavelength of the wave, [tex]\lambda=0.66\ m[/tex]
We need to find the length of the string. Let l is the length of the string. The speed of a transverse wave is given by :
[tex]v=\sqrt{\dfrac{T}{M}}[/tex]
M is the mass per unit length, M = m/l
[tex]v=\sqrt{\dfrac{lT}{m}}[/tex]
[tex]l=\dfrac{v^2m}{T}[/tex]
The velocity of a wave is, [tex]v=\nu\times \lambda[/tex]
[tex]l=\dfrac{(\nu\times \lambda)^2m}{T}[/tex]
[tex]l=\dfrac{(160\ Hz\times 0.66\ m)^2\times 5.5\times 10^{-3}\ kg}{230\ N}[/tex]
l = 0.266 meters
So, the length of the string is 0.266 meters. Hence, this is the required solution.
Answer:
L = 0.275 m
Explanation:
velocity of transverse wave in a stretched string is given as
[tex]v =\sqrt \frac{T}{\mu}[/tex]
where T = tension = 230N
μ = linear density
[tex]μ = \frac[m}{L}[/tex]
where length L is in meters
Velocity = [tex]n\lambda[/tex]
so we have after equating both value of velocity
[tex]\sqrt \frac{T}{\mu} = n\lambda[/tex]
[tex]\frac{T}{\mu} =(n\lambda)^{2}[/tex]
μ = [tex]\frac{T}{(n\lambda)^{2}}[/tex]
μ = [tex] \frac{230}{(160*0.66)^{2}}[/tex]
μ = 0.020 kg/m
but μ = [tex]\frac[m}{L}[/tex]
so length of string is
L = [tex]\frac{5.5*10^{-3}}{0.020}[/tex]
L = 0.275 m
