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  • The fig shows two snap shots, each of a wave travelling along a particular string. The phase for the waves are given by a) 4x-8t b) 8x-16t. Which phase corresponds to which wave in the figure?

The fig shows two snap shots, each of a wave travelling along a particular string. The phase for the waves are given by a) 4x-8t b) 8x-16t. Which phase corresponds to which wave in the figure?

Answers (1)

\\ \text{The standard equation of a plane progressive wave is}\ y=A \sin (k x-w t),\\ $ \text{the phase of the wave is}\ $(\mathrm{kx}-\mathrm{wt})$\\ (a) Comparing $4 x-8 t$ with $(k x-\omega t),$\\ we get $\omega=8$ and $k=4$ \\ $\therefore \quad \lambda_{1} \quad=\frac{2 \pi}{k}=\frac{2 \pi}{4}=\frac{\pi}{2}$ \\ (b) Comparing $8 x-16 t$ with $(k x-\omega t),\\ $ we get $\omega=16$ and $k=8$ \\ $\therefore \lambda_{2}=\frac{2 \pi}{k}=\frac{2 \pi}{8}=\frac{\pi}{4}$ \\ So, $\lambda_{1}=2 \lambda_{2}, \\ \therefore$ we can say from figure that snap-shots 1 and 2 correspond to a and b respectively.

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shubham.krishnan

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