Question

The string of a musical instrument is $90cm$ long and has a fundamental frequency of $124Hz$. The distance $x$ from one end of the string where it should be pressed to produce a fundamental frequency of $186Hz$

• A. $60cm$
• B. $50cm$
• C. $45cm$
• D. $75cm$

Answer 1

Answer: (A)

$60cm$

The velocity of the travelling wave remains a constant.
Initially for fundamental mode,
the length of the string is half the wavelength.
$\lambda =180cm$
$\nu =124Hz$
The new frequency is Given by: ${\nu }_2=186Hz$
Using the fact that $\nu \lambda =constant$
we get ${\lambda }_2=120cm$
The midpoint of this would be the node (where the string needs to be plucked).
The string needs to be plucked at 60cm.