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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.

Measures of Wave Motion

         

A body of mass \(m = 2\text{ kg} \) is oscillating on a spring. The position in meters of the body as a function of time \(t\) can be expressed as

\[ x(t) = A\cos{(2\pi ft)} \text{ m} .\]

If the phase of \( x(t)\) is shifted by \(\delta = \frac{8 \pi}{5} \text{ rad},\) the time delay of its cycle is \(KT \text{ s},\) where \(T\) is the period of the oscillation. What is the constant \(K?\)

A body of mass \(m = 2\text{ kg} \) is oscillating on a spring. The position of the body in meters as a function of time \(t\) can be expressed ass \[ x(t) = A\cos{(2\pi ft)} \text{ m}. \] If \( x(t)\) is delayed by \(\frac{1}{3}\) of its cycle, what is the phase shift \(\delta\) in radians?

As illustrated in the above diagram, a body of mass \(m = 4 \text{ kg} \) attached to a spring with spring constant \( k = 16 \text{ N/m}\) is oscillating on a frictionless floor. Initially at \(t=0,\) the position of the body was \( x(t=0) = 4 \text{ m } \) and the velocity was \( v(t=0) = 0 \text{ m/s }.\) What is the amplitude of the oscillation?

A body of mass \(m = 2 \text{ kg} \) is oscillating on a spring. The position of the body is given as \( x(t) = 4 \cos{(30 t)} \text{ m}, \) where \(x \) denotes the difference in the length of the spring from its original length. What is the period of the body?

Assume that \(\pi = 3 \).

A normal human can hear the sound frequency from \( 20 \text{ Hz} \) to \( 20000 \text{ Hz}. \) Find the longest wavelength of the hearable sound, given that the speed of sound is \( 340 \text{ m/s}. \)

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