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.
$T=4\mu f^2d^2$
$T=2\mu f^2d^2$
$T=\frac{\mu f^2d^2}{2}$
$T=\frac{\mu f^2d^2}{4}$
A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as:
A transverse wave travels on a taut steel wire with a velocity of ${v}$ when tension in it is $2.06 \times 10^{4} \;\mathrm{N} .$ When the tension is changed to $T$. the velocity changed to $\frac v2$. The value of $\mathrm{T}$ is close to
A wire of $10^{-2} kgm^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of wire such that m rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 ms^{^{-1}}$.
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is
$(a) $ the speed of a transverse wave on the string, and
$(b)$ the tension in the string?
Equation of travelling wave on a stretched string of linear density $5\,g/m$ is $y = 0.03\,sin\,(450\,t -9x)$ where distance and time are measured in $SI$ united. The tension in the string is ... $N$