91影视

Length of the transmission line is L = 347 m .

Linear density of the transmission line is $渭=3.35\mathrm{kg}/\mathrm{m}$.

Tension of the transmission line is T = 65.2 MN .

We can find the frequency of the fundamental mode using the formula for it. Taking the difference between two successive frequencies obtained from the above formula we can the frequency difference between the successive modes.

Formula:

The frequency of nth mode,$f=\frac{nv}{2L}......\left(1\right)$

The speed of the wave, $v=\sqrt{\left(\frac{T}{渭}\right)}........\left(2\right)$

For fundamental mode is n = 1 substituted in equation (1), thus we get the frequency formulas as:

$f=\frac{v}{2L}......\left(3\right)$

Again, using equation (2) and the given values, we het the speed of the wave as given:

$$\begin{gathered} v={\left(\frac{65.2脳{10}^6}{3.35}\right)}^{\frac{1}{2}} \\ =4.4116脳{10}^3\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, substituting the value of equation (3) in equation (1), we get the frequency of the fundamental node as:

$$\begin{gathered} f=\frac{4.4116脳{10}^3}{2脳347} \\ =6.36\mathrm{Hz} \end{gathered}$$

Hence, the required value of fundamental frequency is 6.36 Hz

The frequency difference between two successive modes using equation (1) is given as:

$$\begin{gathered} 鈭�f=f_n-f_{n-1} \\ =n\frac{v}{2L}-\left(n-1\right)\frac{v}{2L} \\ =\frac{v}{2L} \\ =\frac{4.4116脳{10}^3}{2脳347} \\ =6.36\mathrm{Hz} \end{gathered}$$

Hence, the value of frequency difference between two successive modes is 6.36 Hz