Waves

JEE Main level, single correct, medium

54 of 142

Question 54 of 142

The equations of two waves are given by :
y1=5sin⁡2π(x−vt)cm{y}_{1}=5\sin 2\pi \left(x-vt\right)cm
y2=3sin⁡2π(x−vt+1.5)cm{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 :

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Answer: (A) 2cm2cm

Given equations can be written as,
y1=5sin⁡(2πx−2πvt)cm{y}_{1}=5\sin \left(2\pi x-2\pi vt\right)cm and
y2=3sin⁡(2πx−2πvt+3π)cm{y}_{2}=3\sin \left(2\pi x-2\pi vt+3\pi \right)cm
From the given equations we can conclude that the phase difference between the waves is 3π3\pi i.e. odd multiple of π\pi. Therefore, destructive interference will happen.
A=∣A1−A2∣=2cmA=\left|{A}_{1}-{A}_{2}\right|=2cm

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