Question

A sinusoidal wave is described by
y(x,t) = 0.4 sin 20.4( x − 95.5 t) cm
where x is the position along the wave propagation. Determine the amplitude, wave
number, wavelength, frequency and velocity of the wave.

Answer 1

Answer on Question#38147 – Physics – Other

A sinusoidal wave is described by

$$y(x,t) = 0.4 \sin 20.4(x - 95.5t) \, \text{cm}$$

where $x$ is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.

Solution:

From the equation:

$$y(x,t) = 0.4 \sin(20.4(x - 95.5t)) \, \text{cm}$$ $$y(x,t) = 0.4 \sin(20.4x - 1948.2t) \, \text{cm}$$

Amplitude: $A = 0.4\,\text{cm} = 0.004\,\text{m}$

Wave number: $k = 20.4\,\text{cm}^{-1} = 2040\,\text{m}^{-1}$

Frequency: $\omega = 1948.2\,\text{Hz}$

To get wavelength:

$$\lambda = \frac{2\pi}{k} = \frac{2\pi}{20.4\,\text{cm}^{-1}} = 0.308\,\text{cm} = 3080\,\mu\text{m}$$

To get wave velocity:

$$V = \lambda \cdot f = \lambda \cdot \frac{\omega}{2\pi} = 3080\,\mu\text{m} \cdot \frac{1948.2\,\text{Hz}}{2\pi} = 9.425 \times 10^6 \frac{\mu\text{m}}{\text{s}} = 9.42\,\frac{\text{m}}{\text{s}}.$$

Answer: $A = 0.004\,\text{cm}$

$$k = 2040\,\text{m}^{-1}$$ $$\omega = 1948.2\,\text{Hz}$$ $$\lambda = 3080\,\mu\text{m}$$ $$V = 9.42\,\frac{\text{m}}{\text{s}}.$$