The transverse displacement y(x, t) of a wave on a string is give… - Vidyadip

MCQ

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}$ This represents a

✓
wave moving in $-x$ direction, speed $\sqrt{\frac{b}{a}}$
B
standing wave of frequency $\sqrt{b}$
C
standing wave of frequency $\frac{1}{\sqrt{b}}$
D
wave moving in $+x$ direction, speed $\sqrt{\frac{a}{b}}$

✓

Answer

Correct option: A.

wave moving in $-x$ direction, speed $\sqrt{\frac{b}{a}}$

a
(a)

$y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}=e^{-(\sqrt{a} x+\sqrt{b} t)^2}$

It is a function of type

$y=f(\omega t+k x)$

$\therefore y(x, t)$ represents wave travelling along

$-x$ direction.

Speed of wave $=\frac{\omega}{k}=\frac{\sqrt{b}}{\sqrt{a}}=\sqrt{\frac{b}{a}}$.

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