Discussion
A steel rod of length 1 m is clamped at its middle . If the fundamental frequency of vibrations is 3 kHz , then the speed of sound in steel is
Answer: B
The speed of sound in steel is \(6000\ \text{m s}^{-1}\).
A rod clamped at its middle has a node at the clamp and antinodes at its two free ends. In the fundamental mode the whole rod is half a wavelength, node in the middle:
\[ \begin{aligned} L &= \frac{\lambda}{2} \Rightarrow \lambda = 2 \times 1 = 2\ \text{m} \\ v &= f\lambda = 3000 \times 2 = 6000\ \text{m s}^{-1} \end{aligned} \]
Taking the rod as a quarter wavelength (as if clamped at one end) gives 12000, not offered. Taking \(\lambda = L\) gives 3000, and the 2000, 4000, 8000 and 9000 values do not follow from either end condition.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development