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  •   Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by</p

 

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by

\mathrm{y=\left ( 10 \cos \pi\;x \sin \frac{2\pi t}{T} \right )}cm

The amplitude of the particle at \mathrm{x=\frac{4}{3}cm} will be _______ cm.

Option: 1

-5 


Option: 2

--


Option: 3

--


Option: 4

--


Answers (1)

best_answer

\mathrm{y=10 \cos (\pi x) \sin \left(\frac{2 \pi t}{T}\right)}
Comparing with general equation

\begin{aligned} &\mathrm{y}=\underbrace {{A \cos (K x) \sin (\omega t)} }_\text{Amplitude}\\ \end{aligned}

\begin{array}{l} \text { Amplitude of the particle at } x=\frac{4}{3} \ cm=10 \cos (\pi x) \\ \text { Amplitude }=A=10 \cos \left(\frac{4 \pi}{3}\right) \\ A=-5 \mathrm{~cm} \end{array} \\ \text{Negative sign denotes downward direction}
 

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rishi.raj

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