Waves

JEE Main level, numerical answer, medium

35 of 142

Question 35 of 142

Two travelling waves produces a standing wave represented by equation. y=(1.0mm)cos⁡[(1.57cm−1)x]sin⁡[(78.5s−1)t]y=\left(1.0mm\right)\cos \left[\left(1.57{cm}^{-1}\right)x\right]\sin \left[\left(78.5{s}^{-1}\right)t\right]. The node closest to the origin in the region x>0x\gt 0 will be at x=......(incm).x=......\left(\text{in}cm\right).

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Answer: 1

At Node,
y=0y=0
⇒cos⁡(1.57x)sin⁡(78.5t)=0\Rightarrow \cos \left(1.57x\right)\sin \left(78.5t\right)=0
⇒cos⁡(1.57x)=0\Rightarrow \cos (1.57x)=0
⇒1.57x=π2\Rightarrow 1.57x=\dfrac{\pi }{2}
⇒x=1cm\Rightarrow x=1cm

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