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  • The equation of two waves are given by : <img alt="\mathrm{y_{1}= 5\, \sin 2\pi \left ( x-vt \right )cm}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By_%7B1%7D%3

The equation of two waves are given by :

\mathrm{y_{1}= 5\, \sin 2\pi \left ( x-vt \right )cm}
\mathrm{y_{2}= 3\, \sin 2\pi \left ( x-vt+1.5 \right )cm}
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

 

Option: 1

\mathrm{2\, cm}


Option: 2

\mathrm{4\, cm}


Option: 3

\mathrm{5.8\, cm}


Option: 4

\mathrm{8\, cm}


Answers (1)

best_answer

\mathrm{y_{1}=5 \sin (2 \pi(x-v t)) \mathrm{cm}}
\mathrm{y_{2}=3 \sin (2 \pi(x-v t+1.5)) \mathrm{cm}.}

By the principle of superposition,the equation of resultant wave is

\mathrm{y= y_{1}+y_{2}}
\mathrm{y= R \sin (K x-\omega t +\theta)}
where ,
\mathrm{R =\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi} }
\mathrm{\phi =\text { phase difference }=3 \pi }
    \mathrm{=\sqrt{5^{2}+3^{2}+2 \times 5 \times 3 \times(-1)} }
\mathrm{R =\sqrt{4}=2 \mathrm{~cm} }

The amplitude of resultand wave is 2 \mathrm{~cm}
The correct option is (1)


 

Posted by

Ritika Kankaria

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