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

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

(e) is correct option.

Step-by-step 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 = (L)/(v)`

`T=(2)/(5000)\ s`

We know that,

The frequency is the reciprocal of time period.

`f=(1)/(T)`

`f=(5000)/(2)`

`f=2500\ Hz`

We know that,

`1\ rad/s =(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.