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← JEE Main 2022 · 24 Jun · Shift 2
PhysicsInteger+4 / -1Question 54 of 90

JEE Main 2022 · 24 Jun · Shift 2, Physics question 54

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
y=(10cos⁡πxsin⁡2πtT)cmy=\left(10\cos\pi x\sin\frac{2\pi t}T\right)\text{cm}
The amplitude of the particle at x=43x=\dfrac43 cm will be ______ cm.

Answer and worked solution

Official answer: 5

Amplitude at xx. A(x)=10∣cos⁡πx∣A(x)=10\left|\cos\pi x\right| cm.

At x=43x=\frac43. cos⁡4π3=−12\cos\dfrac{4\pi}3=-\dfrac12, so A=5A=5 cm.

Answer: 5