Question

There are four samples P, Q, R and S with natural frequencies 64, 96, 128 and 256 Hz, respectively. They are mounted on test setups for conducting vibration experiments. If a loud pure note of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration?

• A. P
• B. Q
• C. R
• D. S

Answer 1

The correct option is C R

Execution frequency;
$f=144Hz$

Natural frequency,
$f_n=64,96,128\text{and}256$

$\therefore \frac{\text{Execution frequency}}{\text{Natural frequency}}$

$=\frac{f}{f_n}=\frac{144}{\underset{\left(P\right)}{64}},\frac{144}{\underset{\left(Q\right)}{96}},\frac{144}{\underset{\left(R\right)}{128}},\frac{144}{\underset{\left(S\right)}{256}}$

$=2.25,1.5,1.25,0.5625$

Since 1.125 is close to 1, so the sample 'R' will show the most perceptible induced vibration.