Waves

JEE Main level, numerical answer, medium

34 of 142

Question 34 of 142

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 \dfrac{2\pi t}{T}\right)cm. The amplitude of the particle at x=43cmx=\dfrac{4}{3}cm will be _____ cm.cm.

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Answer: 5

Amplitude is the maximum displacement from the mean position, for that
sin⁡(2πtT)=1\sin \left(\dfrac{2\pi t}{T}\right)=1
Therefore, A=∣10cos⁡(43π)∣=10×12=5cmA=\left|10\cos \left(\dfrac{4}{3}\pi \right)\right|=10\times \dfrac{1}{2}=5cm

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