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Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWaves2 Marks
Question
For the harmonic travelling wave $\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x}+3.5)$ where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of:
4m
✓

Answer

$\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x+3.5})$
$\text{y}=2\cos(20\pi\text{t}-0.0016\pi\text{x}+7.0\pi)$
Wave is propagated in $+\text{x}$ direction because $\omega\text{t}$ and kx are in with opposite sign standard equation $\text{y}=\text{a}\cos(\omega\text{t}-\text{kx}+\phi)$
a = 2, $\omega=20\pi,\ \text{k}=0.016\pi$ and $\phi=7\pi$
Path difference p =4 m (given) = 400cm
Phase difference $\Delta\phi=\frac{2\pi}{\lambda}\times\text{p}=\frac{2\pi}{\lambda}\times400$
$\Delta\phi=\text{k}\times400=0.016\pi\times400$
Phase difference $\Delta\phi=6.4\pi$ rad.

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