Waves Physics Grade 11

Table of Contents

The Basics of Waves: Waves in Physics

What are waves?

A wave is a medium barrier that carries energy without the pure movement of particles. It can take the form of elastic deformation, pressure variations, electrical or magnetic intensity, electrical potential or temperature. First, waves propagate. Second, waves depend on their environment. For example, a sound wave is no longer just a vibration but an acoustic wave that depends on the wavelength. In our hearing, the pressure wave propagates the sound through the air. Sound waves also depend on their medium: rain and thunder are vibration-derived waves that depend on pressure and distance. Different waves have different qualities. The wavelength of a sound wave is the distance between the places where the vibration occurs. The wavelength of light depends on the temperature.

Types of waves

Two types of waves are distinguished by their amplitude, wavelength and frequency: A standing wave is a wave form in which the oscillation frequency of a wave reaches a peak in every cycle of its passage through the medium. Wave Motion: A wave can be viewed as a material deformations occurring continuously in the waves’ standing waves, according to the temporal and spatial directions of the system’s expansion and contraction. Background: In scientific literature, waves are often referred to as fluids, because of the differences in wavelength and oscillation frequency among different wave modes. For example, sound waves have a wavelength around 10-16 meters, and sound waves are distinguished from seismic waves and lightning by their frequency (how many times per second).

Waves in physics

Types of waves in physics Quasi-static waves: A wave that stays constant against time. These may result from temperature fluctuations in a gas, ions or light passing through a medium. Self-interference waves: Usually produced by two or more mediums with different refractive indexes and short wavelengths. Dynamic waves: If two mediums create two wave fronts, the waves oscillate back and forth in a wavefront for the duration of the event. For example, waves created by traffic or aeroplanes traveling through the air will oscillate at certain frequencies that affect aircraft and the way in which we perceive their size. Static waves: The permanent movement of medium. They are usually produced by two mediums with different refractive indexes. For example, light propagates along a plane.

Conclusion

In my next post I will continue this wave analogy and look at the moving wave example in more detail. I will discuss how it relates to the more popular fluidic models, and why moving waves are not possible. This post has only touched the surface of this complex subject. References Saverio Stranges, Modern Wave Theory, and Everyday Shapes and Forms, Springer, New York, 1992, ISBN: 9780310173607 John Fienberg, The Big Wave Book: Exploring the Science and Magic of Ocean Waves, Gomatrans UK Ltd, London, 1997, ISBN: 9780711724763 “Waves of information,” published online on February 6, 2015, in the Journal of Research in Engineering Statistics, Vol. 1, pp. 1-6 © Copyright 2014 Thomas Gerwin.

Over the past decade, low-intensity extrasporial shock wave therapy (LESWT) has emerged as a treatment for erectile dysfunction (ED). To better understand the differences between the various devices used to treat ED, physicians must understand the basic physics of the various shock wave generators.

What is the difference between progressive and stationary waves?

Progressive Waves

1. Waves which first produced in a medium and then travels through it from one point to another are called progressive waves”
2. We can say that the type of waves that propagate through a medium is known as progressive waves or travelling waves.
3. By dropping a pebble in a quiet stationary pool of water a disturbance is produced at the point of impact of stone to the water. It spreads out in all four directions on the surface of the water in a patterned way with the same speed.
4. These waves transfer the energy from one point to the other point so we can say that they act a carrier of energy as well.

Stationary Waves

1. “When two plane waves having the same amplitude and frequency, traveling with the same speed in opposite direction along a line, are superposed, a wave obtained is called stationary or standing waves”

2. These waves consist of a combination of nodes and antinodes produced back to back in a certain order.

3. Most string and wind musical instruments produce sound because of the formation of stationary waves or standing waves in these instruments. Vibrations in these instruments produce stationary waves of definite frequency.

4. These waves cannot serve as a source to transfer energy. Due to the production of nodes and antinodes, the amplitude of the wave becomes zero after half cycle.

Q.2 Clearly explain the difference between longitudinal and transverse waves.

Transverse Waves

1. “Those waves in which the particles of the medium vibrate along a bar perpendicular to the path of propagation of the waves are understood as transverse waves”

2. The vibration of the particle is perpendicular to the direction of propagation of the wave.

3. Transverse waves can propagate with or without a medium.

4. It consists of crusts and troughs.

5. Examples of transverse waves are waves produced in water or stretched string etc.

Longitudinal or Compression Waves

1. “Those waves in which particles of the medium vibrate around their mean work along the direction of propagation of the waves are reached longitudinal or compression waves”

2. The particles of the medium vibrate parallel to the direction of propagation of the wave.

3. Longitudinal waves can only propagate in a medium.

4. It consists of compression and rarefaction.

5. Examples of the longitudinal waves include sound waves and earthquake waves etc.

Q.3 A careful student says that he can predict the frequency of spring mass system even though he knows that how far the spring stretches when the mass is hung from it. How he justifies himself?

Answer:
As the time period of a mass-spring system is given as,

Q.4 Is there a transfer of energy through a medium when a stationary wave is produced in it, explain?

Answer:
No there is no transfer of energy through a medium when a stationary wave is produced in it.
Reason:
As we know that a stationary wave consists of a combination of nodes and anti-nodes but at points of nodes, the amplitude of the wave becomes zero i.e. they are at rest and have no displacement from the mean position. Therefore, they cannot transfer energy at this point or these points will be cut points to the transfer. So stationary waves cannot be used as a source for the transfer of energy.

Q.5 Two wave pulses traveling in opposite direction completely cancel each other as they pass. What happens to the energy possessed by the waves?

Answer:
When two wave pulses travelling in opposite direction completely cancel each other on passing then standing waves produced in result.

As standing waves consists of nodes and anti-nodes, so at node points, the amplitude becomes zero and so as the energy. Therefore, particles at node points will be at rest so possess no energy at all. There will be no transfer of energy at these points but only the conversion of energy from one form to another i.e. from kinetic energy to potential energy.

At anti-nodes the energy will be potential energy while at mean position it will be kinetic energy.

The answer sounds confusing

Q.6 What are the conditions of constructive and destructive interference?

Answer:

Conditions for Constructive Interference:

“When two waves arrive at the same place at the same time in phase, then they reinforce each other and constructive interference occur”

Such type of interference takes place when the crust of one wave falls on the crust of another wave and similarly trough to trough. This can only be possible if the path difference between the superposition of waves at any point must be equal to the integral multiple of their wavelength.

i.e. Path Difference = 0, λ, 2λ, 3λ, 4λ, 5λ, …………….

P.D = nλ

Where, n = 0, 1, 2, 3, 4, ………………….

and, λ = wavelength of the waves

Conditions for Destructive Interference:

“If two waves arrive at the same place at the same time but are out of phase (180^o), then destructive interference takes place”

Such type of interference takes place when the crust of one wave falls on the trough of another wave. This can only be possible if the path difference between the superposition of waves at any point must be equal to an an odd integral multiple of their wavelength. Given as,

Path Difference = λ/2, 3λ/2, 5λ/2, 7λ/2, …………….

Where, n = 0, 1, 2, 3, 4, ………………….
and, λ = wavelength of the waves

Q.7 How might one can locate the position of nodes and anti-nodes in a vibrating string?

Answer:
We can locate nodes and anti-nodes in a vibrating string as

1. At nodes points the string has maximum tension and zero amplitude. As these points are at rest so we see string as a combination of loops and at the end of every loop, there is a node point.

2. Similarly, at points of anti-node points in a vibrating string have minimum tension and maximum amplitude. As in every loop, the tension is maximum at mid points so these points will be anti-node points. Or anti-node points can be above or below to that mean point in mid.

Q.8 Is it possible for an object which is vibrating transversely to produce sound wave?

Answer:
Yes it is possible for an object which is vibrating transversely to produce sound waves. This phenomena can be visualized in all musical devices which use strings to produce sound.

When player beats the strings of instrument, he actually is producing the transverse waves and as transverse waves are good source to transfer energy so energy will travel with them through air in form of sound waves which are longitudinal in nature.

Q.9 Why does a sound wave travel faster in solid than in gases?

Answer:
As speed of sound wave through a medium is given by,

Where, E = Elasticity of the medium
and ρ = Density of medium
But for solids, ‘E’ is taken as young’s modulus of the solid. Whereas for gases it is bulk modulus.
We know that density of solids are greater than that of gases and also the young’s modulus of solids has greater value than the bulk modulus of the gases. So the term ‘E/ρ’ will give greater value for solids as compared to gases i.e. ‘v’ will have greater value for solids than gases.
Therefore, sound wave travel faster in solid than in gases.

Q.10 Why does the speed of a sound wave in a gas changes with temperature?

Answer:
As speed of sound wave through a medium is given by,

Where, E = Elasticity of the medium
and ρ = Density of medium
This equation tells us that velocity of sound has an inverse relation with density of the medium i.e. denser the medium, lower will be the velocity.

As we know that a rise in temperature of a gas increases the distance between the gas particles. As a result the density of the gas will decrease. Therefore, the velocity of sound will increase through the gas with decrease in density.

Similarly, when the temperature of a gas decreases then its volume will decrease and so the particles will get closer to each other which results into increase of density. Therefore, the velocity of sound will decrease.

So we can say that the speed of a sound wave in a gas changes with temperature.

Q.11 Is it possible for two astronauts to talk directly to one another even if they remove their helmets?

Answer:
No it is not possible for two astronauts to talk directly to one another on removing of their helmets.
Reason:
We know that sound waves are longitudinal mechanical waves in nature, so they need a material medium in order to propagate or to travel. However, in space there is no material medium between two astronauts so they cannot talk with each other without helmet.

Q.12 Estimate the frequencies at which a test tube 15 cm long resonates when you blow across its lips?

Answer:
Given Data:
Length of tube = L = 15 cm = 0.15 m
Consider speed of sound = v = 340 ms^-1
To Find:
Frequencies = f₁, f₂, f₃, ………., f_n = ?
Solution:
Here test tube acts as closed pipe and we know that frequency for closed pipe is given as,

Where, n = 1, 2, 3, 4, …….., n
So frequency of first harmonic will be given by putting n = 1 in equation (1) as follows,

Putting values, we get

Or,
f₁ = 567 Hz
Now, second harmonic is given by,
f₂ = 3f₁ = 3 × 567 Hz
f₂ = 1701 Hz
And third harmonic will be,
f₃= 5f₁ = 5 × 567 Hz
f₃= 2835 Hz
If we keep on calculating, then n^th harmonic will be,
f_n = (2n-1) f₁ = (2n-1) 567 Hz