Question

1. The frequency obtained from a plucked string is 400HZ when the tension is 2N. Calculate (a) the frequency when the tension is increased to 8N, (b) the tension needed to produce a note of frequency 600HZ.

Answer 1

Answer:

a)1600HZ,b)3N

Explanation:

a)If 1N=200HZ so,2N×8N

2×8=1600HZ

b)If 1N=200HZ so,600HZ/2N

600/2=3N

Answer 2

Answer:

When the tension is increased to 8N the frequency will be 800Hz.

The tension needed $4.5N$ to produce a note of frequency 600HZ.

Explanation:

According to the formula,

$f=\frac{\sqrt{T} }{L}$

where,

f is the frequency,

T is the tension and

L is the length of the string.

Now,

It is given,

plucked string is 400HZ and the tension is 2N.

$400=\frac{\sqrt{2} }{L}\\L=400\times \sqrt{2}\\L=400\sqrt{2} Ns^{-1}$

Case-(a)

$\frac{f_1}{f_2} =\frac{\frac{\sqrt{T_1} }{L_1} }{\frac{\sqrt{T_2} }{L_2} }$

$\frac{f_1}{f_2} =\sqrt{\frac{T_1}{T_2} } \times \frac{L_2}{L_1}$

$\frac{400Hz}{f_2} =\sqrt{\frac{2N}{8N} } \\f_2=400\times 2\\f_2=800Hz$

when the tension is increased to 8N the frequency will be 800Hz.

Case-(b)

When the frequency will be, 600Hz.

$\frac{f_1}{f_2} =\frac{\frac{\sqrt{T_1} }{L_1} }{\frac{\sqrt{T_2} }{L_2} }$

$\frac{f_1}{f_2} =\sqrt{\frac{T_1}{T_2} } \times \frac{L_2}{L_1}$

$\frac{400Hz}{600Hz} =\sqrt{\frac{2N}{T_2} }$

Square both the side,

$(\frac{2Hz}{3Hz})^{2} ={\frac{2N}{T_2} }\\T_2=2\times \frac{9}{4} \\T_2=\frac{9}{2}\\T_2=4.5N$

The tension needed $4.5N$ to produce a note of frequency 600HZ.

To know more about tension, follow the link given below,

https://brainly.in/question/666748

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