Types of Waves and Their Properties

Longitudinal waves travel only in the elastic medium. These waves comprise of compressions and rarefactions. The speed of Longitudinal waves is given by :

$v=\dfrac{\sqrt{B}}{\rho }$ where B is the bulk modulus of elasticity and $\rho $ is the density of the medium

The wave equation is y = 2 sin(6pit - 2pix - pi/6). Velocity v = dy/dt = 2 * 6pi * cos(6pit - 2pix - pi/6). Acceleration a = dv/dt = -2 * (6pi)^2 * sin(6pit - 2pix - pi/6). At x=4 and t=1, the argument is 6pi - 8pi - pi/6 = -2pi - pi/6. sin(-2pi - pi/6) = sin(-pi/6) = -1/2. Thus, a = -2 * 36pi^2 * (-1/2) = 36pi^2.

The answers are (B) and (D).

The properties of a medium necessary for wave propagation are its elasticity, low resistance and inertia. 
Ans: D

On the surface of water transverse waves form.
Option "B" is correct.

The electric and magnetic fields have to remain continuous at the refractive index boundary. If the frequency changed, the light at each side of the boundary would be continuously changing it's relative phase and there would be no way to match the fields.
Furthermore, for conservation of energy frequency should remain same.
Energy $E' = h\nu'$ inside the glass must be equal to the energy outside, so
$E = E'$ gives
$h\nu = h\nu'$
so $\nu = \nu'$
the frequency in the medium is equal to that of outside.
Ans: A

When a wave propagates through a gas, the displacement of the particle is parallel to wave propagation. Thus, it's a longitudinal wave. 

Sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. If a sound wave is moving from left to right through air, then particles of air will be displaced both rightward and leftward as the energy of the sound wave passes through it. The motion of the particles is parallel to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.
Hence, the statement is false.

The waves in which the particles of the medium travel in the same direction as the waves are called longitudinal waves. 

$Answer:-$ C option

When a motor boat sails in water , waves will be produced on the surface of the water. We know that water waves are a combination of longitudinal and transverse waves as the particles move in a circular path.    

$Answer:-$ C option

$Answer:-$ A option

In a transverse wave, the displacement of the particle is perpendicular to the wave propagation. Thus, the angle between particle velocity and wave  velocity should be $\pi/2$.

Transverse waves have particles oscillating perpendicular to the direction of motion of wave. Ripple in the surface of water is transverse in nature

Propagation of waves depends on the medium through which they propagate. Transverse wave need a medium rigid enough which neither liquid nor gas can provide and hence transverse wave can travel through metals. For longitudinal wave they just require a medium for propagation. Hence transverse and longitudinal wave can both propagate in metals.

By definition a wave in which the particles of the medium oscillate to and fro about their mean positions in the direction of propagation is known as longitudinal wave. It can be produced in any medium.

In wave motion, particles of the medium vibrate about their mean positions. The particles of the medium do not move from one place to another

Waves produced in a spring by compressing a small portion of it and releasing are longitudinal waves.

Compression and rarefaction are seen in longitudinal waves

In transverse waves, particle of the medium vibrate in a direction perpendicular to the direction of wave motion.

We know that a transverse wave consists of successive crests and troughs. In a  transverse wave, the particles of the medium oscillate in a direction perpendicular to the direction of propagation.

A transverse wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the yz plane. In any pluck string instrument we are actually doing the same.

A transverse wave is a wave that consists of oscillations that are perpendicular to the direction of wave propagation

The correct option is (b)

loaded spring  applies force only in axial direction of the spring and the movement is also axial so the waves produced are longitudinal waves.

the distance between two either consecutive troughs or troughs is called wavelength and between a trough and a immediate crest is half of wavelength .

The pressure in a medium varies as a longitduinal wave passes through the medium

The correct answer is (a)

Transverse wave is that wave which vibrate the particles of medium in the medium in the $\bot $ar direction to the direction of wave propegation.

Velocity of transverse wave ${V _T} = \sqrt {\left( {\frac{T}{m}} \right)} $

In a gas, molecules can only move back and forth in the direction of the wave propagation due to the lack of shear modulus, making the waves longitudinal.

Polarization is a property that requires the oscillation of the medium to be perpendicular to the direction of wave propagation, which is only possible for transverse waves.

In a longitudinal wave, the pressure variation and density variation are both proportional to the displacement gradient, causing them to be in phase with each other.

A longitudinal wave is characterized by the displacement of particles parallel to the direction of wave propagation, creating regions of compression and rarefaction. Crests and troughs are features of transverse waves.

Ultrasound frequency used for imaging is about $5 MHz.$
The corresponding wavelength is $\lambda = \dfrac{v}{\nu}=\dfrac{1540 \text{m/s}}{5\times 10^6} = 0.3mm$ 
Here speed of ultrasound in tissue is taken to be $1540 m/s$.
So ultrasound can not be used for bone fractures as it bone fracture can have size of few microns.
Ultrasound does not travel faster than sound. Sound speed does not depend on frequency.
$v=\nu \lambda$ if $\nu$ is higher, $\lambda$ becomes smaller and $v$ remains constant.

$\begin{array}{l} { f _{ 1 } }=3f \ { f _{ 2 } }=5f \ \Rightarrow 5{ f _{ 1 } }=3{ f _{ 2 } } \ Hence, \ option, , A, , is, , correct, , answer. \end{array}$

When a longitudinal wave reflects from a rigid wall, the displacement node is at the wall, causing a phase change of pi radians.

A stationary wave y = a sin(wt) cos(kx) can be written as the sum of two progressive waves: y = (a/2) sin(wt - kx) + (a/2) sin(wt + kx). Therefore, the amplitude of each component wave is a/2.

A wave traveling along the Y-axis must have its displacement as a function of (y +/- vt). Option A represents a wave where the displacement x is a function of (y - vt).

There are 3 types of mechanical waves
1.Transverse Waves
2.Longitudinal Waves
3.Surface Waves

when the pebble is thrown in water the disturbance created travels in all outwards directions over the surface of the water in the form of ripples these ripples are circular in shape .

When tuning fork is sounded by striking its one end then the prongs vibrate in and out and stem vibrate up and down. Hence, vibration of prongs are transverse and those of stem are longitudinal. 

Transverse waves cannot propagate in a gas because there is no mechanism for driving motion perpendicular to the propagation of the wave.

Water waves are both longitudinal and transverse. As a wave travels throught he water, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water.

When we pluck the wire of a sitar, the wave produced in the wire are transverse wave.

Slinky is a dress which is tight-fitting, elastic and flexible. By fixing one end on a rigid support and holding the other end waves can be generated. By moving it back and forth, longitudinal waves can be generated. By moving up and down, transverse can be made.

Water surface exhibits a combination of both longitudinal and transverse waves. When the wave travels through the water, the particles travel in a circular path, both parallel and perpendicular to the direction of wave propagation. 

Amplitude and frequency depend on source and as frequency is different, wavelength also has to be different to maintain same speed as speed is constant for a medium in a particular condition.

Ultrasonic wave , Infrasonic wave and Seismic wave are longitudinal waves

Velocity of transverse wave $v =\sqrt{\dfrac{T}{\mu}}$

All waves can be classified into two categories . They are Transverse and longitudinal waves

The phenomenon of polarization confirms that light is a transverse wave because for polarization, the light should have different components oscillating in the different planes and a transverse wave has the oscillations perpendicular to the direction of propagation of the wave.

At nodes in longitudinal waves,there is maximum compression, So, there will be pressure.

Transverse waves require a restoring force due to shear stress, which is present in solids but absent in fluids (liquids and gases).

The apparent speed of sound with wind is (v + vw). The frequency f remains constant. Since v_apparent = f * lambda_prime, we have (v + vw) = f * lambda_prime. Since v = f * lambda, f = v/lambda. Thus, lambda_prime = (v + vw) / (v/lambda) = ((v + vw) / v) * lambda.

In case of light, the waveform changes perpendicular to the relative motion. So, it is a type of transverse wave, which causes the medium to vibrate perpendicular to the wave energy .

light is a EM wave and has transverse nature .

A longitudinal wave is a wave that consists of oscillations that are perpendicular to the direction of wave propagation

The correct option is (b)

in longitudinal waves at compressions density is high and at rerefactions the particle density is low.