Small amplitude progressive wave in a stretched string has a speed of $100 \mathrm{cms}^{-1}$, and frequency…

Small amplitude progressive wave in a stretched string has a speed of $100 \mathrm{cms}^{-1}$, and frequency $100 \mathrm{~Hz}$. The phase difference between two points $2.75 \mathrm{~cm}$ apart on the string, in radians, is
  1. 0
  2. $11 \frac{\pi}{2}$
  3. $\frac{\pi}{4}$
  4. $\frac{3 \pi}{8}$

Solution

$\begin{aligned} & \text { Given; } \mathrm{f}=100 \mathrm{~Hz}, \mathrm{v}=100 \mathrm{~cm} \mathrm{~s}^{-1}=1 \mathrm{~ms}^{-1}, \\ & \Delta \mathrm{x}=2.75 \mathrm{~cm}=2.75 \times 10^{-2} \mathrm{~m}, \text { Phase difference } \\ & \Delta \phi=? \\ & \Delta \phi=\frac{2 \pi}{\lambda} \Delta \mathrm{x}=\frac{2 \pi}{\frac{\mathrm{v}}{\mathrm{f}}} \times \Delta \mathrm{x}[\because \mathrm{v}=\mathrm{f} \lambda] \\ & \text { or, } \Delta \phi=\frac{2 \pi \times 2.75 \times 10^{-2}}{1} \times 100=\frac{11}{2} \pi\end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 1)

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