Question 4: Waves

Question

A steel rod 100 cm long is damped at into
middle. The fundamental frequency of
longitudinal vibrations of the rod are given
to be 2.53 kHz. What is the speed of sound
in sound is steel?

Accepted Answer

In fundamental mode, $$l=2\left(\frac{\lambda}{4}ight)=\frac{\lambda}{2}$$
$$\Rightarrow \quad \lambda=2 l$$ ..... (i)
Given, $$l=100 \mathrm{~cm}, v=2.53 \mathrm{~kHz}=2.53 	imes 10^3 \mathrm{~Hz}$$
We know that,
$$\begin{aligned}
v & =v \lambda \
& =v 	imes 2 l \quad 	ext{[from Eq. (i)]}\
& =2.53 	imes 10^3 	imes 2 	imes 100 	imes 10^{-2} \
& =5.06 	imes 10^3 \mathrm{~m} / \mathrm{s} \
& =5.06 \mathrm{~km} / \mathrm{s}
\end{aligned}$$

Answer

6.2 km/s

Answer

5.06 km/s

Answer

7.23 km/s

Answer

7.45 km/s

Waves

A steel rod 100 cm long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in sound is steel?

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