A string of length 2 ~m is fixed at both ends. If this string vib… - Vidyadip

MCQ

A string of length $2 \mathrm{~m}$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 \mathrm{~Hz}$ then the waves would travel on its with a velocity of

A
$125 \mathrm{~m} / \mathrm{s}$
B
$250 \mathrm{~m} / \mathrm{s}$
✓
$500 \mathrm{~m} / \mathrm{s}$
D
$1000 \mathrm{~m} / \mathrm{s}$

✓

Answer

Correct option: C.

$500 \mathrm{~m} / \mathrm{s}$

(c) For string $\lambda=\frac{2 l}{p}$where $p=$ No. of loops ($=$ Order of vibration)
Hence for forth mode $p=4\Rightarrow\lambda=\frac{l}{2}$
Hence $(v=n\lambda=500\times\frac{2}{2}=500 \mathrm{~Hz})$

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