A rope of length $L$ and mass $M$ hangs freely from the ceiling. If the time taken by a transverse wave to travel from the bottom to the top of the rope is $T$, then time to cover first half length is
$T$
$T\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right)$
$\frac{T}{\sqrt{2}}$
$\frac{T}{2}$
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 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 steel wire with mass per unit length $7.0 \times 10^{-3}\,kg\,m ^{-1}$ is under tension of $70\,N$. The speed of transverse waves in the wire will be $.........m/s$
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
One end of a long string of linear mass density $8.0 \times 10^{-3}\;kg m ^{-1}$ is connected to an electrically driven tuning fork of frequency $256\; Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \;kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0,$ the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along positive $y$ -direction. The amplitude of the wave is $5.0\; cm .$ Write down the transverse displacement $y$ as function of $x$ and $t$ that describes the wave on the string.