into distinct groups.
P r o p e r t i e s o f electromagnetic waves
l Do not carry any charge.
l Do not deflected by electric and magnetic field.
l Travel with speed of light in vacuum.
lFrequency does not change when it goes from one medium to another, but its wavelength
changes.
lTransverse in nature.
l Do not require any material medium for propagation
Modified Ampere’s law
This law implies the fact that not only a conduction current but a displacement current, associated with a changing electric field, also produces a
magnetic field
BRAIN
ELECTROMAGNETIC WAVE
Ra iod Microwave Infrared Visible Ultraviolet X-rays Gamma rays
Radiowaves l Used in radio
communication .
Infrared lUseful for elucidating
molecular structure.
lU s e f u l f o r h a z e photography.
Ultraviolet l Can cause many chemical
reactions,e.g.,the tanning of the human skin.
l Ionize atoms in atmosphere, resulting in the ionosphere.
Gamma rays l In the treatment of
cancer and tumours l To produce nuclear
reaction X-rays
l Penetrate matter (e.g., radiography) l Ionize gases
l Cause fluores encec
l Cause photoelectric emission from metals
Microwaves lRadar communication lAnalysis of fine details
o f m o l e c u l a r a n d atomic structure.
Visible light lDetected by stimulating
nerve endings of human retina.
lCan cause chemical reaction.
Displacement current
It is the current which is produce when electric fieldd and hence electric flux
changes with time.
ELECTROMAGNETIC WAVE
An electromagnetic wave is wave radiated by ana accelerated charge as coupled electric and magnetic field oscillating perpendicular to each other and to the direction of propagation of wave.
Magnitude of and are related as
Speed of anelectromagneticwave in free space is given by
Y
E B E B
E B E B
Direction of propagation
X
Maxwell’s four equations
James Clerk Maxwell made great strides in helping to understand electromagnetism and produced a unified model of electromagnetism. His research in kinematics and electricity laid
foundation for modern quantum mechanics and special relativity.
James Clerk Maxwell
Vibrations of A closed organ Pipe
In a closed organ pipe, one end is closed and other end is open.
In a closed organ pipe, the closed end is always a node while the open end is always an antinode.
Fundamental mode, or first mode λ1 = 4L where L is the length of the pipe.
Fundamental frequency υ1=λv1=4v
L where v is the speed of sound in air.
This frequency is called first harmonic.
Second mode, λ2 4
= L3 Frequency,
υ2 λ υ
2 3 1
4 3
= v = v =
L This frequency is called
third harmonic or 1st overtone.
Third mode, λ3 4
= L5 Frequency,
υ3 λ υ
3 5 1
4 5
= v = v =
L This frequency is
called fifth harmonic or second overtone.
υ1 : υ2 : υ3 = 1 : 3 : 5
Only odd harmonics are present.
For nth mode, λn L
= n4− 2 1
( )
Frequency, υn λ υ
n
v v n
L n
= = (2 1− = −) ( )
4 2 1 1
where n = 1, 2, 3, ....
This frequency is called (2n – 1)th harmonic or (n – 1)th overtone.
Vibration of An open organ Pipe In an open organ pipe, both ends are open.
In an open organ pipe, at both ends there will be antinodes.
Fundamental mode or first mode, λ1 = 2L where L is the length of the pipe.
Fundamental frequency υ1=λv1=2v
L where v is the speed of sound in air.
This frequency is called first harmonic.
Second mode, λ2 = L Frequency,
υ2 λ υ
2 2 1
= v = =v
L This frequency is called
second harmonic or first overtone.
Third mode, λ3 2
= L3
Frequency, υ3 λ υ
3 3 1
2 3
= v = v =
L This frequency is
called third harmonic or second overtone.
υ1 : υ2 : υ3 = 1 : 2 : 3
Hence in open pipe all harmonics are present, whereas in a closed pipe only odd harmonics are present.
For nth mode, λn L
= 2n
Frequency, υn λ υ
n
v nv
= =2L n= 1, where n = 1, 2, ...
This frequency is called nth harmonic or (n – 1)th overtone.
The fundamental frequency of an open organ pipe is twice that of a closed organ pipe of the same length.
If an open pipe of length L is half submerged in water, it will become a closed organ pipe of length half that of open pipe as shown in figures (a) and (b). So its frequency will become
v v
L v
L v
C=4( / )2 =2 = O.
i.e., equal to that of open pipe, i.e., frequency will remain unchanged.
End correction
The antinode at the open end of a pipe is not formed exactly at the open end but a little outside. This is called the end correction. This is denoted by e and is given by e = 0.6r
where r is the radius of the pipe. If L is the length of pipe then for closed pipe L is replaced by L + e while for open pipe L is replaced by L + 2e.
Due to the end correction the fundamental frequency of a closed organ pipe is given by
υC v
L e v
L r
=4[ + =] 4[ +0 6. ]
Due to the end correction, the fundamental frequency of an open pipe is given by
υO v
=2[L e+2] = +v
L r
2[ 1 2. ] Speed of sound in air at room temperature using resonance tube is given by
v = 2υ(L2 – L1) where,
υ = frequency of the tuning fork L1 = first resonance length L2 = second resonance length End correction e L= 2−3L1
2 SELFCHECK
13. A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m s–1.
(a) 4 (b) 12
(c) 8 (d) 6
(JEE Main 2014) Beats
When two waves of nearly equal (but not exactly equal) frequencies travelling with same speed in the same direction superpose on each other, they give rise to beats.
Beat frequency : It is defined as number of beats heard per second.
Beat frequency = no. of beats/sec = (υ1 – υ2)
= difference in frequencies.
Applications of the Phenomenon of Beats
The phenomenon of beats is used to determine
•
frequency of a tuning fork.
The phenomenon of beats is used in tuning of
•
musical instruments.
The phenomenon of beats is used in detecting the
•
presence of dangerous gases in mines.
The phenomenon of beats is used in radio reception
•
in many ways.
Tuning fork is a source of sound of single frequency and frequency of a tuning fork of arm length L and thickness d in the direction of vibration is given by
υ= r r
= =
d
L v d L
Y v Y
2 2
where Y is the Young’s modulus and r is the density of the material of the tuning fork.
KEYPOINT
Loading a tuning fork with wax decreases its
•
frequency while filing a tuning fork increases its frequency.
Doppler’s Effect
When a source of sound or an observer or both are in relative motion, there is an apparent change in the frequency of sound as heard by the observer. This phenomenon is known as Doppler’s effect.
According to Doppler’s effect the apparent frequency heard by the observer is given by
′ = ±
υ υ v vv v os
where vs, vo and v are the speed of source, observer and sound relative to air.
The upper sign on vs (or vo) is used when source (observer) moves towards the observer (source) while lower sign is used when it moves away.
If the wind blows with speed vw in the direction of sound, v is replaced by v + vw in the above equation.
If the wind blows with speed vw in a direction opposite to that of sound, v is replaced by v – vw in the above equation.
When a source is revolving in a circle and observer is stationary outside, as shown in the figure.
At ,A max v v vs
υ υ
= − At ,C min v
v vs
υ υ
= + Beat frequency = υmax – υmin.
There is no Doppler effect at B and D.
When an observer is revolving in a circle with a stationary source outside, as shown in the figure.
At , ( )
A max v v vo υ = + υ
At , ( )
C min v v vo υ = − υ Beat frequency = υmax – υmin.
There is no Doppler effect at B and D.
If source and observer both are stationary i.e.
vs = vo = 0 then υ′ = υ. Similarly, if source and observer both are moving in the same direction with same speed,
i.e. vs = vo, then υ′ = υ. Thus it is clear that if there is no relative motion between the source and the observer then there is no Doppler effect.
SELFCHECK
14. A train is moving on a straight track with speed 20 m s–1. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 m s–1) close to
(a) 18% (b) 24%
(c) 6% (d) 12%
(JEE Main 2015) 15. A bat moving at 10 m s–1 towards a wall sends a
sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = 320 m s–1)
(a) 8258 (b) 8516
(c) 8000 (d) 8424
(JEE Main 2015) AnswEr kEys (sElf chEck)
1. (a) 2. (a) 3. (c) 4. (b) 5. (a) 6. (b) 7. (c) 8. (c) 9. (c) 10. (d) 11. (d) 12. (a) 13. (d) 14. (d) 15. (b)
nn