A sonometer wire of resonating length 90 ~cm has a fundamental fr… - Vidyadip

MCQ

A sonometer wire of resonating length $90 \mathrm{~cm}$ has a fundamental frequency of $400 \mathrm{~Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600 \mathrm{~Hz}$ under same tension________.$\mathrm{cm}$.

A
$30$
B
$40$
C
$50$
✓
$60$

✓

Answer

Correct option: D.

$60$

d
$\mathrm{f}_0=400 \mathrm{~Hz} ; \mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}=\text { constant }$

$\frac{\lambda}{2}=\mathrm{L} ; \mathrm{v}=\mathrm{f}_0 \lambda$

$\frac{\mathrm{v}}{2 \mathrm{f}_0}=\mathrm{L} \Rightarrow \mathrm{v}=2 \mathrm{Lf}_0$

$\mathrm{~L}^{\prime}=\frac{\mathrm{v}}{2 \mathrm{f}^{\prime}}=\frac{2 \mathrm{Lf}_0}{2 \mathrm{f}^{\prime}}$

$=\frac{L f_0}{\mathrm{f}^{\prime}}=\frac{90 \times 400}{600}=60$

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