The transverse displacement y(x, t) of a wave on a string is given by y(x, t)=e-(a x2+b t2+2 √a b x t) This represents a :

Question

The transverse displacement y(x, t) of a wave on a string is given by y(x, t)=e-(a x2+b t2+2 √a b x t) This represents a : (A) Standing wave of frequency (1/√b) (B) Wave moving in +x direction with speed √(a/b) (C) Wave moving in -x direction with speed √(b/a) (D) Standing wave of frequency √b

Tardigrade Admin · Accepted Answer

y(x, t)=e-(√a x+√b t)2 This is a wave travelling in -x direction with speed (√b/√a)

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

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

Wave moving in $+ x$ direction with speed $\frac{a}{b}$

Wave moving in $- x$ direction with speed $\frac{b}{a}$

Standing wave of frequency $b$

$y (x, t) = e^{- (a x + b t)^{2}}$
This is a wave travelling in $- x$ direction with speed
$\frac{b}{a}$

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

Standing wave of frequency b​1​

Wave moving in +x direction with speed ba​​

Wave moving in −x direction with speed ab​​

Standing wave of frequency b​