The distance between two consecutive points with phase difference of $60^{\circ}$ in wave of frequency 500…

The distance between two consecutive points with phase difference of $60^{\circ}$ in wave of frequency 500 Hz is 0.6 m . The velocity with which wave is travelling is
  1. $1.8 \mathrm{~km} / \mathrm{s}$
  2. $9 \mathrm{~km} / \mathrm{s}$
  3. $3.6 \mathrm{~km} / \mathrm{s}$
  4. $2.7 \mathrm{~km} / \mathrm{s}$

Solution

$\phi=60^{\circ}=\frac{\pi}{3}$
Path difference is given by, $\begin{array}{ll} \quad \mathrm{x} & =\frac{\lambda}{2 \pi} \times \phi \\ \therefore \quad 0.6 & =\frac{\lambda}{2 \pi} \times \frac{\pi}{3} \\ \therefore \quad \lambda & =3.6 \mathrm{~m} \\ \quad v & =\mathrm{n} \lambda=500 \times 3.6=1800 \mathrm{~m} / \mathrm{s}=1.8 \mathrm{~km} / \mathrm{s} \end{array}$ .

Asked in: MHT CET 2024 (04 May Shift 1)

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