Question

A. Una onda armónica que se propaga por un medio unidimensional tiene una frecuencia de 500Hz y una velocidad de propagación de 350m/s. ¿Qué distancia mínima hay en un cierto instante, entre dos puntos del medio que oscilan con una diferencia de fase de π/3?

Answer 1

Answer:

0.117 m

Explanation:

First of all, we can find the wavelength of the wave in the problem, by using the wave equation:

$v=f\lambda$

where:

v = 350 m/s is the speed of the wave

f = 500 Hz is the frequency of the wave

$\lambda$ is the wavelength

Solving for $\lambda$,

$\lambda=\frac{v}{f}=\frac{350}{500}=0.7 m$

This means that the distance between two consecutive points of the wave having a difference of phase of

$\phi=2\pi$

is 0.7 m.

Here we want to find the distance between two points that have a difference of phase of

$\phi'=\frac{\pi}{3}$

So, we can set up the following rule of three:

$\frac{d}{\phi}=\frac{d'}{\phi'}$

where d' is the distance we are looking for. Solving for d',

$d'=d\frac{\phi'}{\phi}=(0.7)\frac{\pi/3}{2\pi}=\frac{1}{6}(0.7)=0.117 m$