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Question
A sonometer wire having a length of 1⋅50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?
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Solution
Given:
Length of the sonometer wire (L) = 1.50 m
Let the
\[\text{ first harmonic be f_0 and thesecond harmonic be f_1 }.\]
According to the question,
\[f_1 = 256 \text{ Hz }\]
,\[\text{ 1st harmonic for fundamental frequency, f_0 = \frac{f_1}{2} = \frac{256}{2} = 128 Hz}\]
When the fundamental wave is produced, we have:
\[\frac{\lambda}{2} = 1 . 5 m\]
\[ \Rightarrow \lambda = 3 m\]
\[\text{ Wave speed, } v = f_0 \lambda\]
\[ \Rightarrow v = 128 \times 3 = 384 m/s\]
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