Question

The equation of a wave is $$ y(x, t)=(3.5 \mathrm{cm}) \sin \left\\{\frac{\pi}{3.0 \mathrm{cm}}[x-(66 \mathrm{cm} / \mathrm{s}) t]\right\\} $$ Find (a) the amplitude and (b) the wavelength of this wave.

Short answer

Answer: (a) The amplitude of the wave is \(3.5 \mathrm{cm}\). (b) The wavelength of the wave is \(6.0 \mathrm{cm}\).

Step-by-step solution

Identify the amplitude of the wave.

The amplitude of the wave is the coefficient of the sine function. In our given equation, the amplitude is \(3.5 cm\).

Identify the wave number.

The wave number, \(k\), has the units of length\(^{-1}\) and is the coefficient of the term inside the sine function. From the given equation, we can find \(k = \frac{\pi}{3.0 \mathrm{cm}}\).

Calculate the wavelength.

The wavelength, \(\lambda\), can be found using the relationship \(\lambda = \frac{2\pi}{k}\). Substituting the wave number we found in Step 2, we get: \(\lambda = \frac{2\pi}{\frac{\pi}{3.0 \mathrm{cm}}} = 2 * 3.0 \mathrm{cm} = 6.0 \mathrm{cm}\).

Final answers

(a) The amplitude of the wave is \(3.5 \mathrm{cm}\). (b) The wavelength of the wave is \(6.0 \mathrm{cm}\).