Answer :
Answer:
266.14532 Hz
60
Explanation:
m = Mass of string = 4.5 g
T = Tension = 765 N
L = Length of string = 0.6 m
f = Frequency = 16 kHz
Linear density is given by
[tex]\mu=\dfrac{m}{L}\\\Rightarrow \mu=\dfrac{4.5\times 10^{-3}}{0.6}\\\Rightarrow \mu=0.0075\ kg/m[/tex]
Fundamental frequency is given by
[tex]f'=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}\\\Rightarrow f'=\dfrac{1}{2\times 0.6}\sqrt{\dfrac{765}{0.0075}}\\\Rightarrow f'=266.14532\ Hz[/tex]
The fundamental frequency is 266.14532 Hz
The number of loops is given by
[tex]n=\dfrac{f}{f'}\\\Rightarrow n=\dfrac{16000}{266.14532}\\\Rightarrow n=60.11753[/tex]
The number of loops is 60.
The Frequency will be "266.14 Hz" and the number of loops are "60".
Given:
Tension,
- 765 N
Length,
- 0.600 m
Mass,
- 4.50 g
As we know,
→ Linear density, [tex]\mu = \frac{Mass}{Length}[/tex]
By substituting the values, we get
[tex]= \frac{4.5\times 10^{-3}}{0.6}[/tex]
[tex]= 7.5\times 10^{-3} \ kg/m[/tex]
The fundamental frequency will be:
→ [tex]F = \frac{1}{2L}\sqrt{\frac{T}{\mu} }[/tex]
[tex]= \frac{1}{2(0.6)}\sqrt{\frac{765}{7.5\times 10^{-3}} }[/tex]
[tex]= 266.14 \ hz[/tex]
and,
The number of loops will be:
→ [tex]n = \frac{f'}{f}[/tex]
[tex]= \frac{16000}{266.14}[/tex]
[tex]= 60[/tex]
Thus the above response is correct.
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