Question

A guitar string is $90\, cm$ long and has a fundamental frequency of $124\, Hz$. To produce a fundamental frequency of $186\, Hz$, the guitar should be pressed

• A. $60\,cm$
• B. $30\,cm$
• C. $20\,cm$
• D. $10\,cm$

Answer 1

Answer: (A)

$60\,cm$

Answer 2

Here, $L_{1}=90\,cm$, $\upsilon_{1}=124\,Hz$, $\upsilon_{2}=186\,Hz, L_{2}$ =? According to the law of length, $\upsilon_{2}L_{2}=\upsilon_{1}L_{1}$ $\therefore L_{2}=\frac{\upsilon_{1}L_{1}}{\upsilon_{2}}=\frac{124\times90}{186}$ $=60 \, cm$