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Classical Mechanics

# Traveling Waves

When a plane wave travels in a medium, the displacements of particles are given by $y= 3 \sin{\left(2\pi(5t-0.02x)\right)} ,$ where $$x$$ and $$y$$ are in meters, and $$t$$ is in seconds. Find the wave velocity.

A tuning fork vibrating at $$68 \text{ Hz}$$ produces a sound wave which travels in air at a speed $$340 \text{ m/s}.$$ Find the distance traveled by the sound during the time the fork makes $$47$$ vibrations.

When a plane wave travels in a medium, the displacements of particles are given by $y= 2 \sin{\left(16 \pi t-0.05 \pi x + \frac{\pi}{2}\right)},$ where $$x$$ and $$y$$ are in centimeters, and $$t$$ in seconds. Find the approximate displacement of the particle at the point $$x= 2 \text{ cm}$$ at $$t= 1 \text{ s}.$$

The source of a sound vibrates according to the equation

$y= 6 \cos{(6 \pi t)}.$

If it sends out waves of velocity $$v= 21 \text{ m/s},$$ what is the wavelength $$\lambda$$ of the waves?

When a plane wave travels in a medium, the displacements of particles are given by $y= 2 \sin{\left(10t-0.02 \pi x + \frac{\pi}{12}\right)},$ where $$x$$ and $$y$$ are in meters, and $$t$$ in seconds. Find the distance traveled by the wave during the time the wave makes $$12$$ vibrations.

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