Question

A steel rod of length 100 cm is clamped at the middle. The frequency of the fundamental mode for the longitudinal vibrations of the rod is (speed of sound in steel = 5 km s–1)

• A. 1.5 kHz
• B. 2 kHz
• C. 2.5 kHz
• D. 3 kHz

Answer 1

Answer: (C)

2.5 kHz

Answer 2

Here , L = 100cm $= 1m,v = 5kms^{- 1}$

$= 5 \times 10^{3}ms^{- 1}$

As the rod is clamped at the middle, therefore the middle point is a node. IN the fundamental mode, the antinode is formed at each end as shown in figure.

Therefore, the distance two consecutive antinodes = L =1m

But the distance between two consecutive antinodes is $\frac{\lambda}{2}.$

$\therefore\frac{\lambda}{2} = 1mor\lambda = 2m$

The frequency of the fundamental mode is

$\upsilon = \frac{v}{\lambda} = \frac{5 \times 10^{3}ms^{- 1}}{2m} = 2.5 \times 10^{3}Hz = 2.5kHz$