A string is clamed at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units)
A string is clamed at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units)
- [JEE MAIN 2019]
- A
$60$
- B
$80$
- C
$40$
- D
$20$
Similar Questions
A piano string $1.5\,m$ long is made of steel of density $7.7 \times 10^3 \,kg/m^3$ and Young’s modulus $2 \times 10^{11} \,N/m^2$. It is maintained at a tension which produces an elastic strain of $1\%$ in the string. The fundamental frequency of transverse vibrations of string is ......... $Hz$
A piano string $1.5\,m$ long is made of steel of density $7.7 \times 10^3 \,kg/m^3$ and Young’s modulus $2 \times 10^{11} \,N/m^2$. It is maintained at a tension which produces an elastic strain of $1\%$ in the string. The fundamental frequency of transverse vibrations of string is ......... $Hz$
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- [JEE MAIN 2024]
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- [JEE MAIN 2020]
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A tuning fork of frequency $340\, Hz$ is sounded above an organ pipe of length $120\, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \,m/s$)
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