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Waves

Waves are disturbances that transport energy without transporting mass. Learn the mechanism underlying sound, deep ocean swells, light, and even the levitation of objects in mid air.

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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