## 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

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?

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1 year 2021-08-14T15:26:37+00:00 1 Answers 44 views 0

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’,

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