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A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will - Physics

MCQ

A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will

Options

  •  vibrate with a frequency of 416 Hz

  •  vibrate with a frequency of 208 Hz

  •  vibrate with a frequency of 832 Hz

  • stop vibrating.

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Solution

vibrate with a frequency of 208 Hz

According to the relation of the fundamental frequency of a string
\[\nu = \frac{1}{2l}\sqrt{\frac{F}{\mu}}\]

where
          l is the length of the string
           is the tension
           μ is the linear mass density

We know that ν1 = 416 Hz, l1 = and l2 = 2l.
\[v_1 \propto \frac{1}{l_1}\]
\[ v_1 l_1 = v_2 l_2 \]
\[\left( 416 \right)l = v_2 \left( 2l \right)\]
\[ v_2 = 208 Hz\] 

  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 15 Wave Motion and Waves on a String
MCQ | Q 21 | Page 323
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