Predict/Calculate A wave on a string is described by the...

Predict/Calculate A wave on a string is described by the following equation: $$ y=(15 \mathrm{cm}) \cos \left(\frac{\pi}{5.0 \mathrm{cm}} x-\frac{\pi}{12 \mathrm{s}} t\right) $$ (a) What is the amplitude of this wave? (b) What is its wavelength? (c) What is its period? (d) What is its speed? (e) In which direction does the wave travel?

Predict/Calculate A wave on a string is described by the following equation:
$$
y=(15 \mathrm{cm}) \cos \left(\frac{\pi}{5.0 \mathrm{cm}} x-\frac{\pi}{12 \mathrm{s}} t\right)
$$
(a) What is the amplitude of this wave? (b) What is its wavelength?
(c) What is its period? (d) What is its speed? (e) In which direction
does the wave travel?

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Key Concepts

Wave Propagation Direction

The direction of wave propagation is determined by the sign of the time-dependent term in the phase of the wave equation. When the phase is in the form kx - ?t, it signifies that the wave is traveling in the positive x-direction.

Amplitude

Amplitude is the maximum displacement of the wave from its equilibrium position. It indicates the energy carried by the wave and is given by the coefficient in front of the cosine function in the wave's equation.

Wavelength

Wavelength is the spatial period of the wave—the distance over which the wave's shape repeats. It can be determined from the wave number in the wave function using the formula wavelength = 2?/k.

Period

Period is the time it takes for one complete cycle of the wave to pass a given point. It is related to the angular frequency by the formula period = 2?/?.

Wave Speed

Wave speed is the rate at which the wave propagates through the medium. It can be calculated by dividing the wavelength by the period or by using the ratio of the angular frequency to the wave number.

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