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.
$T=4\mu f^2d^2$
$T=2\mu f^2d^2$
$T=\frac{\mu f^2d^2}{2}$
$T=\frac{\mu f^2d^2}{4}$
The transverse displacement of a string (clamped at its both ends) is given by
$y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$
where $x$ and $y$ are in $m$ and $t$ in $s$. The length of the string is $1.5\; m$ and its mass is $3.0 \times 10^{-2}\; kg$
Answer the following:
$(a)$ Does the function represent a travelling wave or a stationary wave?
$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?
$(c)$ Determine the tension in the string.
If tension in a wire is made four times, then what will be the change in speed of wave propagating in it ?
A perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the pulse will
Write equation of transverse wave speed for stretched string.
The linear density of a vibrating string is $1.3 \times 10^{-4}\, kg/m.$ A transverse wave is propagating on the string and is described by the equation $Y = 0.021\, \sin (x + 30t)$ where $x$ and $y$ are measured in meter and $t$ in second the tension in the string is ..... $N$