A travelling wave moving from left to right has an amplitude of 0.15m, a frequency of 550Hz and a wavelength of 0.01m. The equation describing the wave is A. y = 0.15 sin 200π(x - 5.5t) B. y = 0.15 sin π(0.01x - 5.5t) C. y = 0.15 sin 5.5π(x - 200t) D. y = 0.15 sin π(550x - 0.01t)
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To find the equation describing the travelling wave, we use the general form for a wave moving from left to right:
$$y(x, t) = A \sin(kx - \omega t)$$
where $A$ is the amplitude, $k$ is the wave number, and $\omega$ is the angular frequency.
Given values:
Amplitude $A = 0.15 \, \text{m}$
Frequency $f = 550 \, \text{Hz}$
Wavelength $\lambda = 0.01 \, \text{m}$
Step 1: Calculate the wave number $k$.
The wave number $k$ is given by the formula $k = \frac{2\pi}{\lambda}$.
$$k = \frac{2\pi}{0.01 \, \text{m}} = 200\pi \, \text{rad/m}$$
Step 2: Calculate the angular frequency $\omega$.
The angular frequency $\omega$ is given by the formula $\omega = 2\pi f$.
$$\omega = 2\pi (550 \, \text{Hz}) = 1100\pi \, \text{rad/s}$$
Step 3: Substitute the values of $A$, $k$, and $\omega$ into the wave equation.
$$y(x, t) = 0.15 \sin(200\pi x - 1100\pi t)$$
Step 4: Compare this equation with the given options.
Let's examine option A: $y = 0.15 \sin 200\pi(x - 5.5t)$
Expand the term inside the sine function:
$$200\pi(x - 5.5t) = 200\pi x - 200\pi \times 5.5t$$
$$200\pi \times 5.5 = 1100\pi$$
So, option A becomes:
$$y = 0.15 \sin(200\pi x - 1100\pi t)$$
This matches the equation we derived.
The final answer is $\boxed{\text{A}}$.
