Contents
Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.
What is a Rarer Medium and a Denser Medium?
When a progressive wave travelling in a homogeneous medium meets a surface of separation with another homogeneous medium, a part of the incident wave is transmitted into the second medium. This phenomenon is known as refraction of wave. In refraction, generally, the direction of wave motion changes while the waves cross the interface of two media.
If nearly all of the energy carried by the incident wave enters the second medium, the second medium is called a transparent medium. For light waves, air, water, glass, etc., are transparent media. On the other hand, if a negligible portion of the energy enters the second medium, the second medium is called an opaque medium. For light waves, wood, iron, brick-walls, etc., are opaque media.
Between them ground glass, oily paper, etc., are semitransparent media.
In Fig.
PQ : surface of seperation of two media or the refracting surface
AO : incident ray
O : point of incidence
OB : refracted ray i.e. the ray entering the 2nd medium.
MN: normal at the point of incidence on the retracting surface
∠AOM = i = angle of incidence
∠BON = r = angle of refraction
Laws of refraction: Refraction of waves obeys the following two laws:
- The incident ray, the refracted ray and the normal to the refracting surface at the point of incidence lie on the same plane.
- The ratio of the sine of the angle of Incidence to the sine of the angle of refraction Is a constant. The magnitude of the constant depends on the nature of the two media and the colour of the incident wave.
Mathematically, \(\frac{\sin i}{\sin r}\) = constant (1µ2) where i and r are the angle of incidence and the angle of refraction, respectively, and µ is called the refractive index of the second medium with respect to the first medium.
The second law of refraction is known as Snell’s Law.
The refractive index (1µ2) is also equal to the ratio of the wave velocities in the two media, i.e., 1µ2 = \(\frac{v_1}{v_2}\) : v1 and are respectively the velocities of the waves in the first and the second medium. The medium with a smaller wave velocity is called a denser medium and the medium with greater wave velocity is called a rarer medium.
Rule governing the deviation of a ray: Generally, the direction of wave motion changes at the time of crossing the refracting surface, i.e., the ray changes its direction. The rule of deviation is as follows:
i) When a ray enters a denser medium from a rarer one, the refracted ray bends towards the normal. In this case, the angle of refraction is less than the angle of incidence, i.e., r < i. Clearly. in Fig., the second medium is denser than the first medium.
ii) When a ray enters a rarer medium from a denser one, the refracted ray bends away from the normal. In this case, the angle of refraction is greater than the angle of incidence, i.e., r > i.
Relation between incident and refracted waves
- Due to refraction, the frequency and the time period of waves do not change.
- The wavelength and the wave velocity suffer changes during refraction.
- The phase of the wave does not change during refraction, i.e., the phase difference between the incident wave and the refracted wave is zero.
In this chapter, only the phenomenon of refraction of sound will be discussed.
Refraction of sound
John Tyndall was the first to demonstrate refraction of sound through a balloon filled with carbon dioxide (CO2). The balloon, surrounded by air, behaves like a convex lens of glass surrounded by air for refraction of light. This is because carbon dioxide is heavier than air. If a clock is placed at one side of the balloon [Fig.], the sound rays produced by the clock meet at a particular point on the other side after refraction through the balloon. If we place our ear at that point, the sound of the clock is heard distinctly. But sound will not be heard if we place our ear elsewhere.
It is an important point to note that, the velocity of sound in air is nearly 330 m ᐧ s-1, whereas that in water is about 1500 m ᐧ s-1. As a consequence, unlike in the case of light waves, air is a medium denser than water for sound waves. So, when sound enters water from air, the rays deviate away from the normal. Steel is a still rarer medium, as the velocity of sound in it is about 5000 m ᐧ s-1. A convex-shaped steel lens or water lens placed in air would, thus, show the properties of a concave lens, i.e., would behave as a diverging lens.
Refraction of sound in atmosphere
Effect of temperature : The whole atmosphere over the surface of the earth may be supposed to be divided into layers, one above the other [Fig.]. At day time, the layer of air adjacent to the surface of the earth has the highest temperature and as we move upwards the temperature falls gradually. So, the density of air increases with increase of height from the surface of the earth. Thus, the upper layers of air are denser than the layers near the surface of the earth.
Hence, sound emitted from a source near the surface of the earth gets refracted. While propagating upwards due to refraction, it bends towards the normal at every layer, and eventually travels upwards almost vertically [Fig.]. For this reason, only a negligible portion of the sound emitted from the source reaches a distant listener standing on the surface of the earth, i.e., at day time sound cannot travel a large distance in the forward direction.
Just the opposite happens at night. The density of the lowermost layer of air is maximum because its temperature is minimum. So, sound emitted from a source on the surface of the earth gets refracted while propagating upwards. In this case, sound moves from denser to rarer medium. So it bends away from the normal at every layer [Fig. (b)]. At one stage, total internal reflection occurs and it begins to move downwards. Ultimately, it reaches a listener. So, sound emitted from a distant source can be heard distinctly at night. Sound of a distant train, low voices of persons sitting in a boat floating in the middle of a river, etc., are very clear to our ears at night.
Effect of wind: Generally, the velocity of wind near the surface of earth is less than that in the upper layers. If wind blows from the source to the listener, the wavefronts at the lower levels have comparatively smaller velocities [Fig.]. Hence, the wavefronts bend towards the earth and help the listener to hear the sound. So, under this condition, sound coming from a distant source is heard distinctly.
On the other hand, if the wind blows in the opposite direction, i.e., from the listener to the source, an opposite incident happens. In this case, the wavefronts at the upper levels have comparatively smaller velocities [Fig.(b)]. Hence, the wavefronts bend in the upward direction. So a very negligible portion of the sound can reach a distant listener standing on the surface of the earth. Therefore, under this condition, sound coming from a distant source is not heard distinctly.