MCQ
A string is stretched between two rigid supports separated by $75 cm$. There are no resonant frequencies between $420 Hz$ and $315 Hz$. The lowest resonant frequency for the string is
- A$210 Hz$
- B$180 Hz$
- ✓$105 Hz$
- D$1050 Hz$
✓
Answer
Correct option: C.
$105 Hz$
(c) : Let $315 Hz$ be the $n^{\text {th }}$ harmonic of the string
$So _1, \frac{n v}{2 l}=315$....(i)
$
\frac{(n+1) v}{n}=420..(ii)
$
Dividing equation (ii) by (i),
$
\begin{aligned}
& \therefore \quad \frac{(n+1) v}{n}=420 \\
& 315 n+315=420 n \Rightarrow n=3 \\
& \text { So, lowest frequency }=\frac{v}{2 l}=\frac{315}{n}=105 Hz
\end{aligned}
$
$So _1, \frac{n v}{2 l}=315$....(i)
$
\frac{(n+1) v}{n}=420..(ii)
$
Dividing equation (ii) by (i),
$
\begin{aligned}
& \therefore \quad \frac{(n+1) v}{n}=420 \\
& 315 n+315=420 n \Rightarrow n=3 \\
& \text { So, lowest frequency }=\frac{v}{2 l}=\frac{315}{n}=105 Hz
\end{aligned}
$
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