Question

a travelling wave in a string is represented by y = 3 sin(π/2t -π/4x) . the phase difference between two particles separated by a distance 4cm is​

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

A travelling wave in a string is represented by y = 3 sin(π/2t -π/4x) . the phase difference between two particles separated by a distance 4cm is

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• y = 3sin(π/2t - π/4x)
• Two particles separated by distance (x) = 4cm

$\large\underline{\underline{\sf To\:Find:}}$

• Phase difference (∅)

Wave Equation is

$\large{\boxed{\bf \red{y=Asin(\omega t+kx) }}}$

On comparing with the given Equation

A = 3

${\sf \omega = \dfrac{π}{2}}$

k =${\sf \dfrac{π}{4}}$

✪$\large{\boxed{\bf \blue{v=A\omega} }}$

$\implies{\sf v = 3×\dfrac{π}{2} }$

$\implies{\bf \green{v=\dfrac{3π}{2}} }$

✪$\large{\boxed{\bf \blue{\lambda =\dfrac{v}{\omega}} }}$

$\implies{\sf \lambda = \dfrac{3π/2}{π/2} }$

$\implies{\bf \green{ \lambda = 3cm }}$

✪${\boxed{\bf \blue{Phase\: Difference (\phi)=\dfrac{2π}{\lambda}×x}}}$

$\implies{\sf \dfrac{2π}{3}×4 }$

$\implies{\sf \dfrac{8π}{3}}$

$\implies{\bf \red{Phase\: Difference (\phi)=\dfrac{8π}{3}}}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Phase difference between two particles separated by a distance 4cm is ${\bf \red{\dfrac{8π}{3}}}$.

Answer 2

Answer:

pie

Explanation:

the formula used is ¢=2π .∆x /lamda

lamda =2π/k

here,A sin (wt - kx)

hence.k= π/4

therefore lamda =2π÷π\4 =8

finally...phase difference =2π .4 (given distance) / 8

answer= π

may this help you..