Traveling Waves

         

When a plane wave travels in a medium, the displacements of particles are given by y=3sin(2π(5t0.02x)), y= 3 \sin{\left(2\pi(5t-0.02x)\right)} , where x x and y y are in meters, and tt is in seconds. Find the wave velocity.

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

When a plane wave travels in a medium, the displacements of particles are given by y=2sin(16πt0.05πx+π2), y= 2 \sin{\left(16 \pi t-0.05 \pi x + \frac{\pi}{2}\right)}, where x x and y y are in centimeters, and tt in seconds. Find the approximate displacement of the particle at the point x=2 cm x= 2 \text{ cm} at t=1 s. t= 1 \text{ s}.

The source of a sound vibrates according to the equation

y=6cos(6πt). y= 6 \cos{(6 \pi t)}.

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

When a plane wave travels in a medium, the displacements of particles are given by y=2sin(10t0.02πx+π12), y= 2 \sin{\left(10t-0.02 \pi x + \frac{\pi}{12}\right)}, where x x and y y are in meters, and tt in seconds. Find the distance traveled by the wave during the time the wave makes 12 12 vibrations.

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