• Describe the basic characteristics and nature of waves

• State fundamentals of sound and its Properties

• Understand geometrical and physical properties of light

• Solve problems involving wave, sound and light

Energy propagation by means of a disturbance in a medium instead of the medium itself is called wave motion.

A stone dropped into a pool of water creates a disturbance, which spreads out in concentric circles. A small floating stick some distance away bobs up and down as the disturbance passes. Energy has been transferred from the point of impact of the stone into the water to the floating stick. This energy is passed along by the agitation of neighbouring water particles. Only the disturbance moves through the water. The actual motion of any particular water particle is comparatively small.

The speed of sound is fastest in solids, followed by that in liquid and is the slowest in air.

In a transverse wave, the  vibration of the individual particles of the medium is perpendicular to the direction of wave propagation. Examples of this type of wave are light waves and water waves.

In a longitudinal wave, the vibration of the individual particles is parallel to the direction of wave propagation. Examples of longitudinal waves are sound waves and waves in a coil (also known as a slinky) when the vibration is applied length wise.

A wave (whether transverse or longitudinal) can be represented by a displacement-distance  graph,  Fig 2.  The  maximum  displacement of each  particle  from  its undisturbed position is the amplitude of the wave. The wavelength (λ) of a wave is the linear distance between two adjacent points on it, which are in phase.

If the frequency (f) of the wave is the number of cycles per second, then the period (T) of the wave is 1/f. 

The reflected  sounds from large surfaces are called echoes. Walls and other solid objects  cause the sound to be heard by the observer's ear a little later than when it started.

Sometimes  the  sound  of  a  speaker's voice in a hall may become blurred because reflected  sound  from  surfaces  such  as  the roof and walls of the hall reaches the listener several times over, each one a fraction of a second later than the one before it.

Echoes may be used to record  the  depth  of the seabed. A sound transmitter is fastened  to the hull of a ship and this sends sound waves vertically downwards through the water (Fig 3). 

The speed of sound in sea water is about 1535 m s-1 and the echo from the sea bed is picked  up  by a microphone attached at a point near to the transmitter a short time after  the sound is transmitted. Both instruments are connected to a recorder which measures  accurately  how  long  the  sound has taken for the double journey, thus allowing the depth of the seabed to be calculated. 

Exercises

1. A longitudinal wave has a frequency of 200 Hz and a wavelength of 4.2 m. What is the speed of the waves? [ 840 m s-1 ]

2. Radio station KDKA in Pittsburgh sends out radio waves with a frequency of 1020 kHz. The speed of radio waves is 3.0 x 108 m s­-1. Find the wavelength of the waves sent out by this station. [ 294.1 m ]

3. A pulse of sound is transmitted from a ship and after reflection from the seabed, arrives back at the transmitter 0.6 sec later. If the speed of sound in sea water is 1500 m s-1, find the depth of the seabed at that point.  [ 450 m ]

4. A man standing between two vertical walls, L m apart, fires a shot. If the first echoes from the nearer and farther walls reached him 0.4 s and 0.8 s respectively, where was he standing and what is the distance between the walls? Velocity of sound is 340 m s-1. [450 m]   [ 1/3 L from the nearer wall,  204 m ]

Sound

1. The frequency of middle C is 256. Taking the velocity of sound in air to be 330 m s-1, what is the wavelength of this note?  [ 1.29 m ]

2. If the velocity of sound in air is 340 m s-1, calculate (a) the wavelength when the frequency is 2000 Hz, (b) the frequency when the wavelength is 85 cm.   [ 0.17 m, 400 Hz ]

3. If the velocity of a radio wave is 3 x 108 m s-1, and a given radio programme is quoted as ‘wavelength 1500 m’ , find the frequency of this transmission. [ 200 kHz ]

4. Taking the velocity of sound in water to be 1450 m s-1, find the depth of water under avessel’s keel if an echometer signal is received after an interval of 3.6 s.  What is the wavelength if the frequency of transmission is 26 kHz ?  [ 2610 m , 5.58 cm ]

5. A ship tracking a submarine sends pulsed ultrasonic waves that are reflected by the submarine. The reflected waves are detected 4.26 s after emission by the tracking ship.  How far is the submarine from the ship? The speed of ultrasonic waves in seawater is 1520 m s-1.  [3238 m]

6. An observer a certain distance from a cliff fires a shot and hears the echo after 3 s.  He walks 165 m nearer to the cliff and this time the corresponding interval is 2 s.  Calculate the velocity of sound and his original distance from the cliff.    [ 330 m s-1, 495 m ]

7. A launch approaching a cliff and gives a short blast by radar when it is 1 km from the cliff. The echo reaches the launch after 5.7 s. If the speed of sound is 340 m s-1, what is the speed   of the launch in m s-1?  [10.9 m s-1]

8. A launch approaching a cliff at reduced speed sounds a short blast and the echo is heard after 10 s.  Five minutes after sounding the first blast she again sounds a blast, and the echo  is heard after 8 s.  What is the speed of the launch?Velocity of sound = 330 m s-1. [ 1.1 m s-1 ]

Ousephp.335 The pitch of an approaching car ambulance siren is higher than the pitch of a receding siren. This phenomenon is the Doppler effect (Fig.4). Other examples are the sound of approaching boats, trains and airplanes.

Exercises

1. The whistle from a Stationary Ship has a frequency of 690 Hz. What is the frequency heard by a personal in an approaching speedboat if velocity of the boat is 15 ms-1. Speed of    sound is 340 ms-1.  [(720 hz)].

2. A train whistle has a frequency of 1000 Hz.  If the train is speeding at a velocity of  80 km h-1 past a stationary railroad-crossing attendant, what is the apparent frequency 

(a) as the train approaches him ? 

(b) as it moves away from him? Assume the velocity of sound in air to be 340 m s-1.  [ 1070 Hz, 939 Hz ]

3. The noon whistle at a textile mill has a frequency of 360 Hz.  What are the frequencies heard by the driver of a car travelling at a velocity of 30 m s-1

(a)  as he approaches the mill  ?

(b)  as he passes the mill ?

 The speed of sound is 340 m s-1 [ 391.8 Hz, 328.2 Hz ]

Light

(1)   Light is a form of energy. It stimulates our sense of vision.

(2)   Light is an electromagnetic wave. It is a transverse wave.

(3)   Light can travel through vacuum.

(4)   Light travels with the speed of 3x108 m s-1 (or) 186000 miles per second.

When  light  is  incident on the surface of an object, some of the light is sent back. This  phenomenon is called reflection of light.

(1) The image is of the same size as the object.

(2) The image is virtual.

(3) The image is erect.

(4) The image is laterally inverted.

(5) The image is situated on the line passing through the object and perpendicular to the plane mirror.

(6)  The image is as far behind the mirror as the object is in front.

Concave mirror

If  the  reflecting  surface  of  a  mirror  forms part of the inner surface of a hollow sphere, the mirror is called a concave mirror.

Convex mirror

If  the  reflecting  surface  of  a  mirror  forms part of the outer surface of a hollow sphere, the mirror is called a convex mirror.

Pole of a concave/convex mirror  (P)

The centre of the surface of a concave mirror is called its pole.

The centre of the surface of a convex mirror is called its pole.

Centre of curvature of a concave mirror or a convex mirror  (C)

The centre of  a  sphere, part of whose surface is the concave mirror, is called the centre of curvature of that mirror. 

The  centre  of  a  sphere,  part of whose surface is the convex mirror, is called the centre of curvature of that mirror. 

Principal axis

The line passing through the centre of curvature and the pole of a concave mirror is called the principal axis.

The line passing through the centre of curvature and the pole of a convex mirror is called the principal axis.

Radius of curvature of a concave mirror or a convex mirror (R)

The  radius of a sphere, part of whose surface is the concave mirror, is called the radius of curvature of that mirror.

The  radius of a sphere,  part of whose surface is the convex mirror, is called the radius of curvature of that mirror.

Principal-ray diagrams: graphical method of locating the image formed by a spherical mirror. Principal rays:

1. Ray parallel to the axis.

2. Ray thru the focal point F.

3. Ray along the radius.

4. Ray to the vertex V.

(1) Distances of real object, real image and real focus are positive. Distances of virtual object, virtual image and virtual focus are negative. 

(2) The focal length and the radius of curvature of a concave mirror are positive.  The focal length and the radius of curvature of a convex mirror are negative.

(3) The perpendicular distance measured above the principal axis is positive. 

The perpendicular distance measured below the principal axis is negative.  

Note:

(1) The  sign conventions are necessary to specify (i) the position of image (in front  of or  behind  the  mirror),  (ii)  the  nature  of  image  (real  or  virtual) and  (iii)  the configuration of image (erect or inverted).   

(2) All distances are measured from the pole of the mirror.  

(3) Sign conventions in symbols:    

 (i) Real object      u = + ,  Virtual object   u = - (not used here)

(ii)  Real image      v = + ,  OO’ = + ,  II’ = - ,   m = -

  Virtual image   v = - ,   OO’ = + ,  II’ = +,   m = +

(iii) Concave mirror   f = + , R = +:   Convex mirror  f = - , R = -

Refraction is the bending of light as it passes from one medium to another.

The  ratio  of  the  velocity  of  light  in  air to the velocity of light in a particular medium is called the refractive index of the medium.

In symbols,   n = c/v

where, n = refractive index of the medium,  c = velocity of light in air, v = velocity of light in the medium

1. The incident ray, the refracted ray and the normal all lie in the same plane.

2. When the ray passes from one medium to another, the ratio of  the sine of angle of incidence to the sine of angle of refraction is a constant. (The second law is called Snell's law.)

Light passes through a flat slab of glass. The angle of incidence of the light onto the glass is 30˚. What is the angle with which the light emerges on the other side of the slab?

The light in one medium does not enter the optically less dense medium and is reflected back into the first medium for all angles of incidence greater than the critical angle. This phenomenon is called total internal reflection.

When light passes from denser to less dense medium, total internal reflection occurs if  i ≥ ic

Principal axis of a lens

The  line  joining  the  centres  of  curvature  of two surfaces of a lens is called the principal axis of a lens.

Centre of a lens (P)

A point in the middle of a lens on the principal axis is called the centre of a lens.

Principal focus of convex lens (F)

The rays parallel to the principal axis converge at a point on the principal axis after passing  through  a  convex lens. This point is called the principal focus of convex lens. (It is a real focus.)

Principal focus of concave lens (F)

The rays parallel to the principal axis are divergent after passing through a concave lens. Those divergent rays appear to come from a point on the principal axis. This point is called the principal focus of concave lens. (It is a virtual focus.) 

Focal length of convex/concave lens (f)

The distance  between the centre and focus of convex/concave lens is called the focal length of convex/concave lens.

Lenses of many different types play an important part in our everyday life. Spectacles, cameras, projectors, microscopes  and  telescopes  are  useful optical instruments employing lenses. Two of the most commonly used optical instruments are described in the following paragraph.

Microscopes

When an object is within the focal length of the lens an enlarged virtual image of the  object  is  seen  through  the  lens.  A  convex lens, which can provide such an enlarged image is called a magnifying glass or a simple microscope.

Telescopes

Telescopes are used to make distant objects appear closer. Essentially, telescopes collect and concentrate light energy to form images. This is particularly the case for astronomical telescopes used to view distant stars and galaxies. Smaller telescopes are used to view terrestrial objects, for example, a transit telescope used by a surveyor.  There are two general types of telescopes, refracting telescopes and reflecting telescopes.

Using total internal reflection, light can be piped from one location to another in glass or plastic rods. (see figure) On entering the ''light pipe'', the light undergoes repeated internal reflections and follows the contour of the pipe.

Exercises

1. The angle of incidence of a ray of light passing from air to a transparent medium x is 30° and the angle of refraction is 19°28’. If another ray is incient at 35° on the medium find the angle of refraction.

2. (a) Find the critical angle of a liquid of refractive index 1.32. 

(b) Find the refractive index of diamond of critical angle 24°27’.

3. (a) An object is placed 30 cm from a convex lens of focal length 10cm. Find the position of its image and the magnification. (b) An object is placed 30 cm from a concave lens of focal length 10 cm. Find the position of Its image and the magnification.

4. An object is 30 cm from a lens and its image is formed 10 cm on the same side as the object  from the lens. (a) Find the type of the lens and its focal length.

5. An image which is ten times the size of the object is formed on the wall by a convex lens of focal length 10cm. (a) How far is the object from the lens? (b) How far is the wall from the lens?

6. The index of refraction of n-propyl alcohol is 1.39. Find the speed of light in that medium and the angle of refraction if light comes from air with an angle of incidence of 55°.

7. Find the sine of the critical angle of incidence for an air-water (nw=1.33)  interface.

8. An amateur lens grinder wants to grind a converging lens of crown glass (n = 1.52) with same curvature on both sides and a focal length of 25 cm. What radius of curvature must be grind on each face?

9. A plano-convex lens has a focal length of 30 cm and an index of refraction of 1.50. Find the radius of the convex surface.

10. A glass lens (n = 1.50) has a focal length of +10 cm in air. Compute its focal length in water  (n = 1.33).

Light is an electromagnetic wave. Light waves are characterized by electric and magnetic field.

Electromagnetic  radiation  spans  a  wide  range of frequencies, but light is gently taken  in  mean  electromagnetic  waves  in  or  near the visible region. The visible region  comprises  wavelengths between 4000 Å and 7000 Å (or) 400 nm and 700 nm.  Above and below the visible regions are the ultraviolet and infrared regions respectively.

When  two beams of light cross each other the resultant amplitude and intensity may be different from the sum of those contributed by the two beams acting separately. The modification of intensity obtained by the superposition of two or more beams of light is called interference.

If the resultant intensity is zero or less than the separate intensities it is called destructive interference. If the resultant intensity is greater, it is called constructive interference.

When waves pass through an aperture or pass the edge of an obstacle, waves spread to some extent into the region, which is not directly exposed to the coming waves. This phenomenon is called diffraction. This is due to bending of light.

1. Young's experiment is performed with orange light of λ = 6058 Å. If the fringes are measured with a micrometer eyepiece at a distance 100 cm from the double slit, it is found that 25 of them occupy a distance of 12.87 mm between centers. Find the distance between the centers of two slits. [ 1.129 mm]

2. A double slit with a separation of 0.25 mm between centers is illuminated with green light 5085 Å from a cadmium arc. How far behind the slit must one go and measure the fringe separation and fine it to be 0.80 mm between centers. [ 39.3 cm]

3. Young's experiment is performed with a monochromatic light with a distance between the slits of 0.1 mm and with a screen a distance of 1.2 m from the slits. If the center of the second order bright fringe is located 1.5 mm from the center of the central maximum on the screen, what is the wavelength of the light used? [ 6250 Å]