wave is represented by the equation $y(x, t)=3.2 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t-50 \mathrm{~m}^{-1} \mathrm{x}\right)$. Another wave, with the same wavelength and frequency, has an amplitude of $4.2 \mathrm{~cm}$. If the two waves interfere constructively, then which equation could represent the superposition of the two waves?
A) $y(x, t)=7.4 \mathrm{~cm} \mathrm{sin}\left(1000 \mathrm{rad} / \mathrm{st}+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=7.4 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question

Quizplus · Accepted Answer

When two waves interfere constructively, their amplitudes add up. The original wave has an amplitude of 3.2 cm, and the other wave has an amplitude of 4.2 cm. Adding these gives 7.4 cm. The frequency and wavenumber (related to wavelength) remain the same, so the equation must have the same $1000 \, \text{rad/s} \, t$ and $-50.0 \, \text{m}^{-1} \, x$ terms. Option D matches these criteria.

Wave Is Represented by the Equation y(x,t)=3.2 cmsin⁡(1000rad/st−50 m−1x)y(x, t)=3.2 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t-50 \mathrm{~m}^{-1} \mathrm{x}\right)y(x,t)=3.2 cmsin(1000rad/st−50 m−1x)

Wave Is Represented by the Equation $y(x, t)=3.2 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t-50 \mathrm{~m}^{-1} \mathrm{x}\right)$