Question

Equation of a travelling wave on a string is given by $y=1\left(mm\right)sin(t-x)$. An ant is moving on string with constant speed of $\sqrt{2}$ mm/sec. with respect to string. If at t = 0, ant is at x = 0. Then mark incorrect statements:
(x is in meter and t is in second)

• A. At $t=0$ velocity of ant with respect to ground is $1\hat{i}$ m/sec.
• B. At $t=0$ velocity of ant with respect to ground is $(2\hat{i}+\hat{j})$m/sec
• C. If $t_a$ and$t_v$ are the time taken by ant and distubance at x = 0 respectively to reach a point ($x_0$,0) then $t_a$ < $t_v$
• D. If $t_a$ and$t_v$ are the time taken by ant and distubance at x = 0 respectively to reach a point ($x_0$,0) then $t_a$ = $t_v$

Answer 1

Answer: (A), (D)

The correct options are
A At $t=0$ velocity of ant with respect to ground is $1\hat{i}$ m/sec.
D If $t_a$ and$t_v$ are the time taken by ant and distubance at x = 0 respectively to reach a point ($x_0$,0) then $t_a$ = $t_v$

Eqn of wave : $y=1\left(mm\right)sin(t-x)$

$\therefore$ $[V=1cos(t-x)]$ is the velocity of any particle on wave.

$\therefore$ at $t=0$ & $x=0$

velocity of the ant w.r.t ground will be

$V_a=1\cos (0-0)$

$=1m/s$

Since the ant is attached to the string, The ant behave as one of the particle of the string.

$\therefore t_a=t_V$ will be same.

$\therefore$ Option (A) & (D) is correct.