A travelling wave pulse is given by y=(4/3 x2+48 t2+24 x t+2) where x and y are in metre and t is in second. The velocity of wave is

Question

A travelling wave pulse is given by y=(4/3 x2+48 t2+24 x t+2) where x and y are in metre and t is in second. The velocity of wave is (A) 4 m/s (B) 2 m/s (C) 8 m/s (D) 12 m/s

Tardigrade Admin · Accepted Answer

y=(4/3 x2+48 t2+24 x t+2) We need to convert it into the form of f(k x-ω t) y=(4/3(x2+16 t2+8 x)+2) y=(4/3(x+4 t)2+2) v=(ω/k) Hence v=(4/1)=4 m / s

Q. A travelling wave pulse is given by $y = \frac{4}{3 x ^{2} + 48 t ^{2} + 24 x t + 2}$ where $x$ and $y$ are in metre and $t$ is in second. The velocity of wave is

4 m/s

2 m/s

8 m/s

12 m/s

$y = \frac{4}{3 x ^{2} + 48 t ^{2} + 24 x t + 2}$
We need to convert it into the form of $f (k x - ω t)$
$y = \frac{4}{3 ( x ^{2} + 16 t ^{2} + 8 x ) + 2}$
$y = \frac{4}{3 ( x + 4 t ) ^{2} + 2}$
$v = \frac{ω}{k}$
Hence $v = \frac{4}{1} = 4 m / s$

Q. A travelling wave pulse is given by y=3x2+48t2+24xt+24​ where x and y are in metre and t is in second. The velocity of wave is