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.