One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.
One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.
- A
$T=4\mu f^2d^2$
- B
$T=2\mu f^2d^2$
- C
$T=\frac{\mu f^2d^2}{2}$
- D
$T=\frac{\mu f^2d^2}{4}$
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- [JEE MAIN 2016]
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$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only.
- [AIIMS 2015]
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The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$
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- [JEE MAIN 2022]