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Wave Motion:-

Wave Components

Waves are present everywhere. Whether we recognize it or not, we encounter waves on a daily basis. We experience a variety of waves on daily basis including sound waves, radio waves, microwaves, water waves, visible light waves, sine waves, stadium waves, earthquake waves, cosine waves and waves on a string. Besides these waves we also experience various other motions which are similar to those of waves and are better referred as wavelike. These phenomena include the motion of a pendulum, the motion of a mass suspended by a spring and the motion of a child on a swing. Wave phenomena emerge in unexpected contexts. The flow of traffic along a road can support a variety of wave-like disturbances as anybody who has experienced a slowly moving traffic will know. The beat of your heart is regulated by spiral waves of chemical activity that swirl across its surface. You control the movement of your body through the action of electrochemical waves in your nervous system. Finally, quantum physics has revealed that, on a small enough scale, everything around us can only be described in terms of waves. The universe isn’t really mechanical in nature. It’s made of fields of force. When a radio antenna makes a disturbance in the electric and magnetic fields, those disturbances travel outward like ripples of water in a pond. In other words, waves are fundamental to the way the universe works.

Wave Motion Definition:-

Slinky Wave

A waves motion can be defined as a disturbance that travels through a medium from one place to another. We consider the case of a slinky wave. When the slinky is stretched from end to end and is held at rest, it assumes an equilibrium position which is the position of rest. In order to induce a wave in slinky we first displace a particle of slinky from its position of rest. Wherever we move the coil whether upward or downward, forward or backward, it returns to its original position. But this movement creates a disturbance. If the slinky was moved in a back and forth direction then the disturbance observed in the slinky is called a slinky pulse. A pulse is a single disturbance that moves through a medium form one place to another. However, if the first coil of the slinky is continuously and periodically vibrated in a back-and-forth manner, it induces a repeating disturbance that continues for a longer duration. This disturbance is termed as a wave.

Frequency and Period of Wave:-

Frequency and Time Period of a Wave

The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. The unit of frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz.

The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle.

Types of  Wave Motion:-

Waves come in various shapes and forms. Though the basic characteristics of wave  motion are same and present in all waves but they can be distinguished on the basis of some distinguishing features.

Transverse Wave Mtion:- 

Transverse Wave

The wave in which particles of the medium move in a direction perpendicular to the direction of the wave is called a transverse wave. Now again if we consider the case of a slinky then if it is stretched in a horizontal direction and a movement is produced in the first coil by moving it up and down, energy is transported from left to right. Since the movement of particles is perpendicular to the direction of movemnt of wave so it is an example of traneverse wave.

Longitudinal Wave Motion:-

Longitudinal Wave

The wave in which the particles move in a direction parallel to the direction of the movement of the wave is called a longitudinal wave. As discussed in the last case, in a slinky, once a disturbance is produced, the energy is transported from left to right. The particles of the medium move in a direction parallel to that of the pulse. Hence, such waves are longitudinal waves.

Component of Longitudinal Wave

Waves can also be categorized on the basis of their capability of transferring energy through a vacuum.

Problem (JEE Advanced) :-

A transverse wave y = 0.05sin(20πx – 50πt) in meters, is propagating along +ve X-axis on a string. A velocity of 5 cm/s at t = 0 along the +ve X-axis from a point where x = 5 cm. After 5 s the difference in the phase of its position is equal to

(a) 150π                (b) 250π 

(c) -245π               (d) -5π

Solution :-

At t = 0, x = 5 cm, initial phase of insect

ϕi = (20π) (5) – (50π) (0) = 100π

After 5s insect will move a distance s = vt = 25 cm

So, it will be at X = 30 cm.

Phase at this instant,

ϕf = (20π) (30) – (50π) (5) = 350π

Thus, ∆ϕ = ϕf – ϕi = 350π – 100π = 250π

From the above observation we conclude that, option (b) is correct.

  • In a wavemotion (transverse or longitudinal), particles do not move forward. It is only the disturbance which is communicated from one point to other.

  • Velocity of a particle and velocity of wave are not same. Velocity of particle varies with time while that of wave is constant.

  • Sound belongs to the category of longitudinal weave motion while light belongs to the category of transeverse wavemotion.

  • Sound requires a material medium for its propagation, while light does not do so.

Refer this video for more information on longitudinal waves:-

Electromagnetic wave Motion:-

Waves which are capable of transmitting energy through a vacuum and are produced by the vibration of charged particles are called electromagnetic waves. Light waves are an example of these waves. Electromagnetic waves are produced on Sun and travel to Earth through vacuum. These waves are responsible for the existence of life on Earth.

Mechanical Wave Motion:-

Those waves which cannot transmit their energy through a vacuum and require a medium for same are called mechanical waves. Various examples include sound waves, water waves, slinky waves etc.

Equation of Wave Motion:- 

The wave motion equation can be expressed as

Speed = Wavelength • Frequency

It states the mathematical relationship between the speed (v) of a wave and its wavelength () and frequency (f). Using the symbols v, λ , and f, the equation can be rewritten as

Question 1 :-

Sound waves in a gas are always:

(a) transverse              (b) longitudinal

(c) stationary              (d) waves of electric and magnetic

Question 2 :-

Light belongs to the category of:

(a) transverse wave motion          (b) longitudinal wave motion

(c) none of the above                   (d) (a) and (b)

Question 3 :-

When sound travels from air to water, the quantity that remains unchanged is:

(a) speed            (b) frequency

(c) intensity         (d) wavelength

Question 4 :-

If we throw a stone in a pond of standing water, the waves produced are:

(a) transverse             (b) longitudinal

(c) some other type    (d) (a) and (b)

Question 5 :-

Two waves of same frequency and velocity should have:

(a) same wavelength      

(b) different wavelengths

(c) sometimes same and sometimes different wavelengths

(d) none of the above

Q.1 Q.2 Q.3 Q.4 Q.5






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