Question

Below you are given data about a wave in three different substances.

Answer 1

1) The period of the wave is the same in all media

2) The speed of the wave is different depending on the medium

3) The speed, the direction and the wavelength of the wave changes, while the frequency remains the same

Explanation:

1)

The period of a wave is the time it takes for the wave to do one complete oscillation.

The period of a wave is the reciprocal of the frequency of the wave:

$T=\frac{1}{f}$

where

T is the period

f is the frequency

From the table given, we notice that the wave has always the same frequency in all the three media: since the period depends only on the frequency, this means that the period of the wave in the three media is the same. We can also calculate it, since we know that

f = 350 Hz

so the period is

$T=\frac{1}{350}=2.86\cdot 10^{-3} s = 2.86 ms$

2)

The speed of a wave is given by the wave equation:

$v=f \lambda$

where

f is the frequency

$\lambda$ is the wavelength

In the first medium,

$f=350 Hz, \lambda = 0.75 m$, so the speed is

$v_1 = (350)(0.75)=262.5 m/s$

In the second medium,

$f=350 Hz, \lambda = 0.70 m$, so the speed is

$v_2 = (350)(0.70)=245 m/s$

In the third medium,

$f=350 Hz, \lambda = 0.65 m$, so the speed is

$v_3 = (350)(0.65)=227.5 m/s$

Therefore, we see that the speed of the wave is different due to the medium.

3)

When a wave travels from a medium into another, the following things happen:

- The direction of the wave changes. In particular, the wave bends towards the normal to the interface between the two media if the second medium has a greater optical density, while it bends away from the normal if the second medium has a lower optical density

- The speed of the wave changes. In particular, the wave slows down if the second medium has a greater optical density, while it speeds up if the second medium has a lower optical density

- The frequency of the wave does not change

- Finally, the wavelength of the wave changes. In particular, the wavelength decreases if the second medium has a greater optical density, while it increases if the second medium has a lower optical density.

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