Question

A 2 meter long bar has a longitudinal/axial wave speed of 5,000 m/s. If the bar is fixed at each end, what is the second natural frequency an for this system in rad/s? a. 12,450 b. 14,850 e 15,710 d. 16,800 e. 18,780 f. None of the above

Answer 1

Answer:

The second natural frequency an for this system is 15710 rad/s.

(e) is correct option.

Explanation:

Given that,

Length = 2 m

Wave speed = 5000 m/s

We need to calculate the second natural frequency

Using formula of Time period

$T = \dfrac{L}{v}$

$T=\dfrac{2}{5000}\ s$

We know that,

The frequency is the reciprocal of time period.

$f=\dfrac{1}{T}$

$f=\dfrac{5000}{2}$

$f=2500\ Hz$

We know that,

$1\ rad/s =\dfrac{1}{2\pi}\ Hz$

So, The frequency is in rad/s

$f= 15710\ rad/s$

Hence, The second natural frequency an for this system is 15710 rad/s.