A composition string is made up by joining two strings of differe… - Vidyadip

MCQ

A composition string is made up by joining two strings of different masses per unit length $\rightarrow \mu$ and $4\mu$ . The composite string is under the same tension. A transverse wave pulse $: Y = (6 mm) \,\,sin\,\,(5t + 40x),$ where $‘t’$ is in seconds and $‘x’$ in meters, is sent along the lighter string towards the joint, the percentage of power transmitted to the heavier string through the joint is approximately ..... $\%$

A
$33$
✓
$89$
C
$67$
D
$75$

✓

Answer

Correct option: B.

$89$

b
Power, $P=\frac{1}{2} \mu \omega^{2} A^{2} v$

Amplitude of transmitted wave, $A_{t}=\frac{2 Z_{1}}{Z_{1}+Z_{2}} A=\frac{2 \sqrt{\mu T}}{\sqrt{\mu T}+\sqrt{4 \mu T}} A=\frac{2}{3} A$

Thus, $P=\frac{1}{2} \mu \omega^{2} A^{2} v$

$=\frac{1}{2} \times 4 \mu \times \omega^{2} \times \frac{4 A^{2}}{9} \times \sqrt{\frac{T}{4 \mu}}=\left(\frac{1}{2} \times \mu \times \omega^{2} \times A^{2} \times \sqrt{\frac{T}{\mu}}\right) \times \frac{8}{9}$

$=\frac{8}{9} \times$ Initial power

Thus power transmitted $=\frac{8}{9} \times 100=89 \%$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

An electric field due to a positively charged long straight wire at a distance $r$ from it is proportional to $r^{-1}$ in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii $1 A$ and $2 A$. The ratio of their respective time periods is

Out of gravitational, electromagnetic, Vander Waals, electrostatic and nuclear forces; which two are able to provide an attractive force between two neutrons

In the given figure, a diode $D$ is connected to an external resistance $R = 100 \,\,\Omega$ and an $e.m .f.$ of $3 .5 \,V.$ If the barrier potential developed across the diode is $0.5\, V,$ the current in the circuit will be........$mA$

A body of mass $1000 \ kg$ is moving horizontally with a velocity $6\ m / s$. If $200 \ kg$ extra mass is added, the final velocity $($ in $m / s )$ is:

The ratio of specific charge of an $\alpha $ -particle to that of a proton is

The condition for observing Fraunhofer diffraction from a single slit is that the light wavefront incident on the slit should be

Select the false statement

A flat circular disc has a charge $ + Q$ uniformly distributed on the disc. A charge $ + q$ is thrown with kinetic energy $E$ towards the disc along its normal axis. The charge $q$ will

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

A ship of mass $3 \times {10^7}\,kg$ initially at rest is pulled by a force of $5 \times {10^4}\,N$ through a distance of $3 \,m$. Assume that the resistance due to water is negligible, the speed of the ship is ........... $m/s$