A string of length 1 m fixed at both ends is vibrating in 3^ rd o… - Vidyadip

MCQ

A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ..... $Hz$

A
$200$
B
$250$
C
$300$
✓
$400$

✓

Answer

Correct option: D.

$400$

d
$II{I^{rd}}$ overtone

$\mathrm{f}=\frac{4 \mathrm{V}}{2 \mathrm{L}}=\frac{2 \mathrm{V}}{\mathrm{L}}=\frac{2}{1} \sqrt{\frac{200}{(5 / 1000)}}=2(200)$

$\mathrm{f}=400 \mathrm{\,Hz}$

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