B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 1: ILLUSTRATIONS

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the velocity and amplitude of the component travelling waves. 

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the node closest to the origin in the region $x>0.$

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the antinode closest to the origin in the region $x>0.$

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the amplitude of the particle at $x=2.33 \mathrm{cm}.$