The transverse displacement of a wave on string is given by y( x , t )= e -( ax 2+ bt 2+2 √ ab xt ) , this represents a

Question

The transverse displacement of a wave on string is given by y( x , t )= e -( ax 2+ bt 2+2 √ ab xt ) , this represents a  (A) Wave moving along + x-axis with speed √(a/b) (B) Wave moving along - x-axis with speed √(b/a) (C) Standing wave of frequency √ textitb (D) Standing wave of frequency (1/√ textitb)

Tardigrade Admin · Accepted Answer

General equation of travelling wave is y=f( ax ± bt )=f(x ± vt ) y= e -( ax 2+ bt 2+2 √a b xt )= e -(√a x+√b t)2 So, the wave will be travelling along - x-axis with speed √( textitb/ textita) .

Q. The transverse displacement of a wave on string is given by $y (x, t) = e^{- (a x^{2} + b t^{2} + 2 ab x t)}$ , this represents a _______

Wave moving along + x-axis with speed $\frac{a}{b}$

Wave moving along - x-axis with speed $\frac{b}{a}$

Standing wave of frequency $b$

Standing wave of frequency $\frac{1}{b}$

General equation of travelling wave is
$y = f (a x \pm b t) = f (x \pm v t)$
$y = e^{- (a x^{2} + b t^{2} + 2 ab x t)} = e^{- (a x + b t)^{2}}$
So, the wave will be travelling along - x-axis with speed $\frac{b}{a}$ .

Q. The transverse displacement of a wave on string is given by y(x,t)=e−(ax2+bt2+2ab​xt) , this represents a _______

Wave moving along + x-axis with speed ba​​

Wave moving along - x-axis with speed ab​​

Standing wave of frequency b​

Standing wave of frequency b​1​