Answer:
The fundamental frequency of its vibration is 19.84 Hz.
Explanation:
It is given that,
Length of the string, L = 9 m
Mass of the string, m = 7 g
Mass of the object, M = 4.5 kg
Distance, d = 6 m
We need to find the fundamental frequency (in Hz) of its vibration. The speed of sound in case of string is given by :
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
[tex]v=\sqrt{\dfrac{MgL}{m}}[/tex]
[tex]v=\sqrt{\dfrac{4.5\times 9.8\times 9}{7\times 10^{-3}}}[/tex]
v = 238.11 m/s
Let f is the fundamental frequency (in Hz) of its vibration. It is given by :
[tex]f=\dfrac{v}{2d}[/tex]
[tex]f=\dfrac{238.11}{2\times 6}[/tex]
f = 19.84 Hz
So, the fundamental frequency of its vibration is 19.84 Hz. Hence, this is the required solution.
The fundamental frequency will be "19.84 Hz".
According to the question,
String's length, L = 9 m
String's mass, m = 7 g
Object's mass, M = 4.5 kg
Distance, d = 6 m
We know the relation,
→ Speed of sound, v = [tex]\sqrt{\frac{T}{\mu} }[/tex]
or,
= [tex]\sqrt{\frac{MgL}{m} }[/tex]
By substituting the given values, we get
= [tex]\sqrt{\frac{4.5\times 9.8\times 9}{7\times 10^{-3}} }[/tex]
= [tex]\sqrt{\frac{396.9}{7\times 10^{-3}}}[/tex]
= 238.11 m/s
hence,
The fundamental frequency be:
→ f = [tex]\frac{v}{2d}[/tex]
By substituting the values,
= [tex]\frac{238.11}{2\times 6}[/tex]
= [tex]\frac{238.11}{12}[/tex]
= 19.84 Hz
Thus the response above is correct.
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