A transverse wave is passing through a string shown in figure. Mass density of the string is $1 \ kg/m^3$ and cross section area of string is $0.01\ m^2.$ Equation of wave in string is $y = 2sin (20t - 10x).$ The hanging mass is (in $kg$):-
$40$
$0.2$
$0.004$
$0.00025$
A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.
Which of the following statements is incorrect during propagation of a plane progressive mechanical wave ?
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
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.
Explain which properties are necessary to understand the speed of mechanical waves.