ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.1

W

Syllabus Notes Wave propagation. Nature of motions in longitudinal and transverse progressive waves. Relation between ν, λ and f. Velocity of propagation of mechanical waves along stretched strings or springs and in solids.

Questions will not be set on the equation

( )kxtay −= ωsin , but an understanding of the variation of displacement with time (x constant) and with distance (t constant) in a progressive wave is expected. Factors affecting the speed of propagation. The

expression mTv = and ρ

E (proofs not required).

Introduction Wave’s motion is a process of energy transmission, without transmission of matter and there are different kinds of phenomena we can call them waves. Examples: kinds vibration 1. sound wave air molecules vibrates to and fro 2. water wave water molecules vibrates up and down 3. wave in spring spring molecules 4. earthquakes particles of the earth 5. electromagnetic wave variation of magnetic field and electric field Waves are produced by vibrating sources. For examples, tuning fork sets air molecules in vibrations and produces sound wave; vibrations of an electron produces electromagnetic wave. If the source is stationary, the frequency of the source is equal to the frequency of the wave produced. (I) Wave Propagation

A progressive or travelling wave is the movement of a disturbance from a source which transfers energy and momentum from the source to the places around it. There are 2 types of waves:

Mechanical Waves – required a material medium for their propagation, such as water waves, sound waves, secondary earthquake waves…

Electromagnetic waves – can travel through a vacuum and are transverse variation of electric and magnetic fields. Wave characteristics: 1. A wave transfer energy – there is no net translation of matter. 2. In a mechanical wave, the medium has properties which have inertia and elasticity. These particles

execute oscillations of small amplitude about their equilibrium positions. 3. Each particle oscillates in the same way as its neighbour, but shows a time lag if it is further from the

source of energy. Mechanical Waves: It is produced by a vibrating source in medium. Energy is transmitted by the vibrations of particles in medium, it requires a medium to transmit e.g. sound wave, water wave. There is an interchange of potential energy and kinetic energy among the particles of the medium.

CHAPTER 1

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.2

W There are 2 kinds of mechanical waves: Longitudinal wave Transverse wave (1) Transverse wave The vibration of wave is perpendicular to the direction of propagation, e.g. electromagnetic wave, water

wave. (2) Longitudinal wave The vibration of wave is parallel to the direction of propagation, e.g. sound wave. A. Describing Wave:

(a) & (b) are transverse wave. (c) is longitudinal wave. All these graphs are taken at a particular time t. From (c), if we take → as +ve direction, we can plot the displacement at various distance x of a longitudinal wave.

** Note that at centres of compression & rarefaction the displacement are zero.

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.3

W Equation of wave: At time interval ∆t, no. of wave = f ∆t

λλ ft

tfv =∆

∆=∴ (true for all kind of wave)

T = period = time for one complete oscillation f = frequency = number of oscillation per second

B. Wave Equations: For a particle P, the displacement y varies with time t:

amplitudeA

tAyP

=

−= ωsin

For a particle Q, which lags behind P by a distance x0

−−=

λπ

ω 02sin

xtAyQ

Hence for different particles at distances x from P is:

−−=

λπω xtAy 2sin

If the wave travelled in opposite direction, Q is leading P.

∴

+−=

λπ

ω 02sin

xtAyQ or in general

−=

λπ

ωx

tAy2

sin

C. Huygen’s Construction In 1678, Huygens (Dutch physicist) proposed a theory to explain the motion of wave. He proposed that a source emitted a wavefront. Wavefront is line or a surface on which the vibration has the same phase at all point. Every point on a wavefront may be regarded as a source of secondary spherical wavelets which spread out with the wave velocity. A smooth line joining the most forward part of the secondary wavelets forms the new wavefront.

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.4

W D. Speed of mechanical waves

1. Transverse pulse : yx mTv ∝ , where T = tension & m = mass per unit length

Use the method of dimension,

=

mT

kv , from experiment, k is equal to 1, mT

v =∴

2. Longitudinal pulse : ρEv = , where E = Young’s modulus & ρ = density

In general, mediumofpropertyinertialmediumofpropertyelastic

v =

3. Short wavelength ripples on deep water : ρλγπ2

=v

Where γ = surface tension, λ = wavelength, ρ = density Past Paper Practices M.C. Questions WAVE PROPAGRATION 1. 1980−I−18

The displacement y of a point P on a plucked string varies with time t as shown in the graph above. Which of the following correctly shows the variation of the velocity v of the point P with time? A. B.

C. D.

E.

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.5

W 2. 1986−I−28

Two waveforms X and Y are displayed on a C.R.O. screen. Which of the following statements is correct ? A. X leads Y by a phase difference of π/4. B. X leads Y by a phase difference of π/2. C. Y leads X by a phase difference of π/4. D. Y leads X by a phase difference of π/2. E. There is no phase difference between X and Y. 3. 1990−I−15 A rubber band is of unstretched length l and force constant k. When it is stretched to a length 2 l, the speed of transverse waves on it is v. What will be the speed of transverse waves when it is stretched to a length 3 l ? A. v B. 2 v C. 3v /2 D. 3 v E. 2 v 4. 1990−I−21

A boat travels in shallow water, in which waves of all wavelengths travel at a speed of 4.0 m/s. What is the speed of the boat if the bow wave generated by the boat has an apex angle of 30o ? A. 2.0 m/s B. 2.3 m/s C. 4.0 m/s D. 6.9 m/s E. 8.0 m/s 5. 1991−I−25

Two trains of traveling waves W1 and W2, of the same amplitude, wavelength and speed move in opposite directions. The period of both of the waves is T and their amplitude is A. At time t = t1, the waves W 1 and W2 are as shown in the figure above. Which of the following statements is/are correct ?

(1) The wavelength of the waves is four times the distance MN.

(2) At time t = t 1 + T/4, the displacement at point M is 2A. (3) Point N is a displacement node.

A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.6

W 6. 1992−I−20

Figure (a) shows the positions of equally spaced molecules in a solid lattice. A longitudinal sond wave travels from left to right through the solid. At a certain instant, the displaced positions of the molecules are shown in Figure (b). Immediately afterwards, what will be the directions of motion of particle 1 and particle 7 ? Particle 1 Particle 7 A. to the right to the right B. to the right to the left C. to the left to the right D. to the left to the left E. at rest at rest 7. 1993−I−24

. A displacement-time graph of a particle in a plane progressive wave is shown above. What is the frequency of this wave ? A. 1.43 Hz B. 2 Hz C. 2.22 Hz D. 4 Hz E. 5 Hz 8. 1994−IIA−14(AL)/ 1994−IIA−9(AS)

Figure (a) represents the displacement-position graph of a travelling wave at a certain instant and Figure (b) represents the displacement-time graph of a particle in the wave. The speed of the wave is A. 300 m/s B. 150 m/s C. 1.2 m/s D. 0.6 m/s E. 0.3 m/s

ADVANCED LEVEL PHYSICS AVES

CSKMS AL PHYSICS WAVES 2004 by Leo Chung P.7

W 9. 1995−IIA−12(AL)/ 1995−IIA−7(AS)

The figure shows a sound wave travelling to the right in air. Air particles A and B are at the centre of a compression and a rarefaction respectively. Which of the following gives correctly the directions of motion of A and B at the moment shown ? Particle A Particle B A. to the right to the left B. to the right at rest C. to the right to the right D. at rest to the right E. to the left to the right 10. 1996−IIA−11(AL)

The least separation between two points with a phase difference of π/6 on a progressive wave is 0.05 m. If the velocity of the wave is 150 m/s, the frequency of the wave is A. 125 Hz. B. 250 Hz C. 375 Hz D. 500 Hz E. 1000 Hz 11. 1997−IIA−11(AL)

The above figure shows a transverse wave propagating to the right along a string. At the moment shown, which of the labelled particles has its velocity and acceleration in opposite directions?

A. P B. Q C. R D. S E. T

12. 1998−IIA−11(AL)

The displacement-time graphs of two oscillating particles P and Q are shown below.

Which of the following phase relations between P and Q is correct? A. P leads Q by π/ 4 B. leads Q by π/2 C. P leads Q by π D. Q leads P by π/ 4 E. Q leads P by π/2