Longitudinal and transverse waves - class-XI

Crest and troughs are part of the waves and they will be  moving in the direction of the wave

The correct option is (a)

The distance between two consecutive crests or troughs are equal in a wave and is known as the length of a wave or wavelength

The distance between a crest and an adjacent trough is half the wavelength (lambda/2). Wavelength = speed * time period = 15 * 0.01 = 0.15 m. Half the wavelength is 0.075 m, which is 7.5 * 10^-2 m.

wavelength and amplitude are independent of each other so for any value of amplitude any wavelength can be possible .

The water molecules displace along the propagation direction as well as along perpendicular direction. 

Phase difference between any two particles in a wave determines lack of harmony in the vibrating state of two particles, ie, how far one particle leads the other or lags behind the other. 
Relation of path difference and phase difference is given by
$\Delta \phi=\frac{2\pi}{\lambda}\times \Delta x$
where $\Delta x$ is path difference. 
But path difference between two crests
$\Delta x=\lambda$
Hence, $\Delta  \phi = \frac{2\pi}{\lambda}\times \lambda =2\pi$ 

The waves produced by a motorboat sailing in water are of both transverse and longitudinal type. Transverse waves are produced on the surface and longitudinal waves are produced deep inside the water.

A crest is a point on the wave with the maximum value of upward displacement within a cycle. A crest is a point on the surface wave where the displacement of the medium is the maximum.

Transverse waves can travel only in solids and only along the surface of liquids, but not in the entire liquid. They can't travel in gases.

Heat rays are infra-red rays.

In any wave motion, energy is always transferred to the next particle which is succeeding the previous particle.  In a wave motion, particles are oscillating in a direction perpendicular to the direction of propagation or parallel. Since oscillation is a periodic motion,  we can say that periodic motion is always associated with the wave.  An oscillatory disturbance is always imparted the next and next particle and this is how the disturbance Travels across the particles.  Ordinary waves require a material medium for propagation. But electromagnetic waves do not require any material medium. They can also propagate through vacuum. Thus material medium is not a necessary condition for all wave motions.

During propagation of a plane progressive mechanical wave amplitude of all the particles is equal, particle of the medium execute S.H.M, wave velocity depends upon the nature of the medium and all the particles are vibrating in the different phase.

A full wave cycle consists of a crest and a trough. The distance from a crest to the next trough is exactly half of the full wavelength.

A crest is a point on the wave where the displacement of the medium is at a maximum

The correct option is (a)

For the wave to propogate, it needs a mechanical medium and this uses the molecules of string to propogate the energy


The correct option is (c)

Though the hammer strikes the bell and the bell starts vibrating, these vibrations are then carried out to the atmosphere only by air molecules thereby creating a sound

The correct option is (a)

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The animation at right shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in orange to show that each particle indeed travels in a clockwise circle as the wave passes.

Particles move in circular paths at the surface of a medium and hence form at the boundary of two mediums.

The correct option is (b)

Tsunami waves are water waves and hence have both the elements of transverse and longitudinal.

Thus option (c) is the correct option

Path difference=10m

The particles of medium moves perpendicular to the direction of the propagation of the wave in the case of transverse wave.

In a longitudinal wave, the displacement gradient (dS/dx) represents the strain. At the center of a compression (C) and a rarefaction (R), the displacement is zero, but the magnitude of the strain (the slope of the displacement curve) is equal.

The distance between a crest and a trough is half a wavelength (lambda/2). Given 10m = lambda/2, the wavelength lambda is 20m. Using the wave speed formula v = lambda / T, where T = 4.0s, we get v = 20m / 4.0s = 5.0m/s.

Comparing the wave function at t = 0 and t = 2, the disturbance shifts from f(x) to f(x - 1), which means the wave profile shifted by 1 meter in 2 seconds. The wave velocity is distance divided by time, which is 1 / 2 = 0.5 m/s.

Transverse waves cannot propagate in gases because there are no forces to cause motion perpendicular to the direction of the wave. A transverse wave propagates in a solid because each atom of the solid has an "equilibrium location" where the forces on it from all its neighboring atoms balance. If one atom is pulled out of its equilibrium location by a disturbance, it will tend to be pulled back to that location. However, when it's out of its equilibrium location, it pulls its neighbors out of their equilibrium locations too, and so on down the line. The result is that a transverse wave disturbance propagates through the material.

A transverse wave travels through a medium in the form of crests and troughs.

• MEDIUM SHOULD BE ISOTROPIC: The properties of the medium should be the same in all directions.
  
• ELASTICITY : The medium should have elasticity so that the particles return back to their original positions after being displaced.
  
• INERTIA : This allows the particles to store kinetic energy.
  
• MINIMUM FRICTION : So that the particles oscillate and the wave travels for a sufficiently long time and distance.
  
• these were the properties required for propagation of mechanical waves , so the answer is A and D.

waves can go reflection , refraction and diffraction  like  light being an EM wave performs all these phenomenons.

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases.

electromagnetic waves donot require medium for propagation . light is a EM wave.

with change in medium the wavelength and velocity of wave both are changed but being property of source remains constant and doesnot change.

longitudinal waves are propagated by  propagation of energy by particles of the medium.

when reflection of wave takes place from the denser medium then  it undergoes a phase change of $\pi$ . 

mechanical waves  are waves which needs medium for propogation.. energy is transferred  while propagation from particle to particle of medium.

$1.$ Mechanical transverse waves cannot propagate through all the medium. They can only propagate through solids not in gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

time taken for the whistle to reach the person is $\dfrac{d}{v}$
$=\dfrac{1.5\times 1000}{332}=4.52sec$
$\therefore$ delay of his clock is $4.52s$

when reflection of wave takes place from the denser medium then  it undergoes a phase change of $\pi$ . Since, here in question the phase is not changing so the medium must be rarer.