Waves Test - 73...

A pulse is started at a time t = 0 along the +x direction on a long, taut string. The shape of the pulse at t = 0 is given by function y with
$$y=\begin{cases} \dfrac { x }{ 4 } +1\quad \  for\quad -4 < x \le 0 \\ -x+1\quad for\quad 0 < x < 1 \\ 0       in any other case\end{cases}$$
here y and x are centimeters. The linear mass density of the string is 50 g/m and it is under a tension of 5N.
The shape of the string is drawn at t = 0 and the area of the pulse enclosed by the string and the x-axis is measured. It will be equal to

The phase difference between two waves, represented by $${ y }_{ 1 }={ 10 }^{ -6 }\sin { \left[ 100t+\left( x/50 \right) +0.5 \right]\ m } $$ and $${ y }_{ 2 }={ 10 }^{ -6 }\cos { \left[ 100t+\left( x/50 \right)  \right]\ m } $$. Where $$x$$ is expressed in metre and $$t$$ is expressed in seconds, is approximately

The amplitude of a damped harmonic oscillator becomes halved in $$1$$ minute. After three minutes the amplitude will become $$1/x$$ of initial amplitude where $$x$$ is:

Displacement of particles in a string in x-direction and is represented by y. Account the following expression for y, those describing wave motion are.

A string fixed at one end only is vibrating in its third harmonic. The wave function is $$y(x,t) = 0.02 sin(3.13x) cos(512t)$$, where y and x are in metres and t is in seconds. The nodes are formed at positions

A wave $$10\sin{(ax+bt)}$$ is reflected from dense medium at an origin. If 81% of energy is reflected then the equation of reflected wave is

A tray of mass M = $$10$$kg is supported on two identical springs, each of spring constant k, as shown in figure. When the tray is depressed a little and released, it executes simple harmonic motion of period $$1.5$$s. When a block of mass m is placed on the tray, the period of oscillation becomes $$3$$s.The value of m is

To determine the position of a point like object precisely ______ light should be used.

A wave frequency $$100Hz$$ travels along a string towards its fixed end. When this wave travels back after reflection, a node is formed at a distance of $$10cm$$ from the fixed end. The speed of the wave (incident and reflected) is

The equation of a plane progressive wave is $$y = 0.02 \sin 8 \pi[t - \dfrac{x}{20}].$$ When it is reflected at a rarer medium, its amplitude becomes 75% of its previous value. The equation of the reflected wave is