Waves

Question 1

Wave Motion

Answer 1

Kind of disturbance which travels through a medium due to repeated vibrations of the particles of the medium about their mean positions

Question 2

Propagation of Sound Waves through Air

Answer 2

• A small region in air is likes a spring - As it travell through the air, it compresses or expands it
• If a region is compressed, density increases of the second region causeing the first region density to decrease
• This causes rarefaction and hence shifts it to adjacent region

Question 3

Propagation of sound in a solid

Answer 3

• When an eleastic wave propagates, the atom is displaced from its equilibrium position and a restoring force is developed

Question 4

Transverse Waves

Answer 4

• Waves in which the individual particles of the medium oscillate perpendicular to the direction of wave propagation
• Travel through a liquid medium

Question 5

Longitudinal Waves

Answer 5

• Waves in which the individual particles of the medium oscillate along the direction of wave propagation
• Travel through all media

Question 6

Angular Frequency

Answer 6

Rate of change of phase with time

Question 7

Wavelength

Answer 7

Distance covered by a wave during the time in which a particle of the medium completes one vibration to and fro about its mean position

Question 8

Angular wave number / Propagation constant

Answer 8

Quantity 2pi / lambda (phase change per unit path difference)

Question 9

Wave velocity / Phase velocity

Answer 9

Direction covered by a wave per unit time in its direction of propagation

Question 10

Speed of transverse wave on stretched string

Answer 10

v = root (T / m)

Question 11

Speed of a transverse wave in a solid

Answer 11

v = root (modulus of rigidity (aka shear modulus) / ro)

Question 12

Speed of longitudinal Wave in a liquid or gas

Answer 12

v = root (k / ro)
k = bulk modulus

Question 13

Speed of longitudinal wave in a solid

Answer 13

root (k + 4/3 * shear modulus) / ro)

Question 14

Speed of a longitudinal wave in a solid rod

Answer 14

v = root (Y / ro)

Question 15

Newton’s Formula for speed of sound in a gas

Answer 15

v = root (P / ro)

Question 16

Laplace formula for speed of sound in a gas

Answer 16

v = root (gamma * P / ro)
gamma = Cp / Cv

Question 17

Plane Progressive harmonic wave

Answer 17

If during the propagation of a wave through a medium, the particles of the medium vibrate simple harmonically about their mean positions, then the wave is said to be plane progressive

Question 18

Factors which affect speed of sound in a gas

Answer 18

• Pressure has no effect!
• At constant pressure, v inversely proportional to square root of density
• Travels faster in moist air than dry hair
• Directly proportional to square root of abs. temp

Question 19

Progressive Wave

Answer 19

Wave that travels from one point of the medium to another

Question 20

Angular wave number or Propagation constant

Answer 20

k = 2pi / lambda

Question 21

y(x,t) =

Answer 21

A sin (omega t - kx)
= A sin 2 pi(t / T - x / lambda)
= A sin 2pi/T (t - x / v) = A sin 2pi / lambda (vt - x)

Question 22

Explain Progressive wave

Answer 22

y = A sin (omega t - kx + psi not)
y = Displacement
A = amplitude
omega = angular freq
t = time
k = angular wave number
x = position
psi not = initial phase angle

Question 23

Phase of a wave

Answer 23

Quantity that gives complete information of the wave at any time and at any position

Question 25

Time period of a wave

Answer 25

Time in which the phase of a particle of the medium changes by 2pi

Question 26

Wavelength

Answer 26

Distance between two points which have a phase difference of 2pi at any given instant

Question 27

Particle velocity

Answer 27

Velocity with which the particles of the medium vibrate about their mean positions

Question 28

Wave velocity

Answer 28

Distance covered by a wave in the direction of its propagation per unit time

Question 29

Acceleration amplitude / maximum value of acceleration

Answer 29

a = (2pi / T)^2

Question 30

Particle Acceleration

Answer 30

acceleration (rate of change in speed and direction) of particles

Question 31

Displacement along negative x-axis

Answer 31

y = A sin (omega t + kx)

Question 32

phase formula

Answer 32

2pi (t / T - x / lambda) + psi not

Question 33

Reflection of a wave from a rigid body

Answer 33

It is reflected back with a phase reversal or phase difference of pi radians

Question 34

Reflection of a wave from an open boundary

Answer 34

Suffers no phase change

Question 35

# [](http://) Node

Answer 35

A node is a point along a standing wave where the wave has minimum amplitude

Question 36

Antinode

Answer 36

An antinode wave is a point on a standing wave where the amplitude of the wave is at its maximum

Question 37

Waves during refraction from one medium to another

Answer 37

Suffers no phase change

Question 38

Principle of superposition of waves

Answer 38

When a number of waves travel through a medium simultaneously, the resultant displacement of any particle of the medium at any given time is equal to the algebraic sum of the displacements due to individual waves

Question 39

Constructive interference

Answer 39

When two waves travel in the same direction and are in phase with each other, their amplitude gets added, and the resultant wave is obtained.

Question 40

Destructive interference

Answer 40

* Destructive interference occurs when waves come together so that they completely cancel each other out. * Same amplitude in opposite directions

Question 41

Stationary waves

Answer 41

When two identical waves of same amplitude and frequncy travelling in opposite directions with the same speed along the same path superpose each other, the resultant wave does not travel in the either direction

Question 42

Equation of stationary wave

Answer 42

y = (2A cos kx) sin omega t

Question 43

Characteristics of stationary waves

Answer 43

1. Disturbance does not advance forward 2. All particules, except at nodes, execute SHM 3. Nodes and antinodes 4. Distance between two successive nodes is lambda / 2 5. Amplitudes different at different points 6. Has same wavelength and time period as two component waves

Question 44

Comparison between stationary and progressive waves

Answer 44

-

Question 45

First harmonic / Fundamental frequency

Answer 45

The first harmonic, also known as the fundamental frequency, is the lowest frequency at which a string or air column can vibrate to create a standing wave pattern

Question 46

Normal Modes

Answer 46

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation

Question 47

Sinusoidally

Answer 47

Sinusoidally means relating to, shaped like, or varying according to a sine curve or sine wave

Question 48

Velocity when it vibrates in p segments

Answer 48

Vp = p / 2L (root (T / m))

Question 49

A pipe of length L with one end closed and other end open vibrates with frequencies given by

Answer 49

v = (n + 1/2) mu / 2L Fundamental mode / First harmonic is v = mu / 4L

Question 50

Beats

Answer 50

Periodic variations in the intensity of sound caused by the superposition of two sound waves of slightly different frequencies

Question 51

Beat frequency

Answer 51

Difference in frequencies of two superposing waves (v1 - v2)

Question 52

# [](http://)