Category: Physics Notes PPT

Geostrophic motion is a fluid flow that occurs in a direction parallel to the lines of equal pressures/isobaric in a rotating system, such as the Earth. 

A Geostrophic flow occurs by the balance of the Coriolis force (a force caused by the Earth’s rotation), and the pressure-gradient force (when the friction is low).

Hence in a geostrophic flow, instead of water moving from a high-pressure region to a low-pressure region, it moves along with the lines of equal pressure and this happens because of the Earth’s rotation.

On this page, we will understand what Geostrophic motion, pressure-gradient  force is and Geostrophic flow is all about.

What is a Geostrophic Motion?

From the above text, we understand that water does not flow from a high sea level to a low sea level, it just gets along with the lines of equal pressure. 

The velocity of the flow varies directly with the pressure gradient and conversely with the latitude. 

In practical, observed fluid flow is not strictly geostrophic, though large-scale oceanic and atmospheric movements approach the ideal stage. It means that the geostrophic current usually portrays the actual current within around 10 percent, provided the comparison is made over large areas and there is a little curve in the isobars.

Pressure-Gradient Force

The pressure gradient quantifies the lowering of the atmospheric pressure in an area at a specific time. For instance, gale force winds turn into a light breeze in a specific city after an hour. 

A pressure-gradient force is a relative force that is calculated when there is a difference in pressures. The below diagrams shows the relative pressure difference:

Geostrophic Flow

A geostrophic current is an oceanic current in which the pressure-gradient force is balanced by the Coriolis effect or the Earth’s rotational force. 

The direction of geostrophic flow is parallel to the lines of equal pressure/isobars, with the high-pressure to the right of the flow in the Northern Hemisphere, and the high-pressure to the left in the Southern Hemisphere. 

The concept of Geostrophic current is taken from weather maps, whose isobars show the direction of geostrophic flow in the atmosphere. 

The below image shows that surface currents generally mirror average planetary atmospheric circular patterns:

Geostrophic flow can either be barotropic or baroclinic. A geostrophic current can be assumed as a rotating shallow-water wave with a zero frequency. 

The geostrophic principle is useful for oceanographers because it helps them infer ocean currents from measurements of the sea surface height (by combined satellite altimetry and gravimetry) or from vertical profiles of seawater density taken by ships or autonomous buoys. 

Do You Know the Examples of Geostrophic Currents?

Examples of Geostrophic Currents

The major currents of the world’s oceans, like the Gulf Stream, the Agulhas Current, and the Antarctic Circumpolar Current,  the Kuroshio Current are all approximately in geostrophic balance and hence they are considered examples of geostrophic currents.

Concept of Geostrophic Motion

You may think about how an oceanographer changes overestimations of the surface slope into a current speed. The premise supposition will be that when we take a gander at the huge flows oversized of 100 km or more there is a considerable balance between two forces – the pressure gradient and the Coriolis force.

Now, let’s understand the concept of Geostrophic flow through ocean currents.

Ocean Currents

Now, talk about the ocean current.

Imagine for a moment (an ideal situation) that there is a ‘high’ and a ‘low’ level in the sea surface (an altimeter can measure this( and that there is no Coriolis effect. 

In the absence of Coriolis force, water would naturally flow from the high to the low region in order to restore the equilibrium. In other words, there is a force that pushes the water from the high level to the low level – and if this force lies proportionally to the difference in levels, then it is the ‘pressure-gradient ’.

Now, considering that Coriolis force occurs on the water. Now, it will pull the current to the right in the Northern hemisphere (as shown in the figure below) and to the left in the Southern hemisphere.

Geostrophic Balance

A time comes when the pressure-gradient force becomes equal to the Coriolis force, the balance between these two forces on a parcel of the water is what we state as the Geostrophic balance. The below image represents the above statement:

So, when the situation is the same as depicted in the figure above, we say that there is a geostrophic balance and that the current is purely geostrophic.

The best part is, an oceanographer can compute the current by the measurement of the slope.

So, let’s understand the Geographic Wind in brief.

Geostrophic Wind                   

The geostrophic wind is a theoretical wind directed along with isobars, i.e., the lines of constant pressure at a given height. This balance rarely holds exactly in nature. 

However, the real wind somewhat differs from the geostrophic wind (imaginary wind) because of the other forces such as friction from the ground. 

From the above diagram, we see the deviation of a real wind from its original path; however, geostrophic wind seamlessly flows without getting affected by any force.

Do You Know?

The suspicion that there is geostrophic balance is just precise when we take a gander at the large-scale flows, for example at scales bigger than a few tens of km. All the significant currents can be considered geostrophic to a first estimate. 

At more limited sizes, the geostrophic (non-geostrophic) segments of the flows, for example, because of the force by the neighborhood wind, become increasingly significant. 

In several coastal areas, the dissemination is to a great extent geostrophic. An altimeter can anyway still be utilized to measure the geostrophic part.

Before moving on to Hall effect derivation, students must note that the Hall effect is the production of the voltage difference. It is caused across an electric conductor and is transverse to this electric current. It essentially refers to the product of magnetic induction and current density when a magnetic field works perpendicular to the current flow associated with a thin film. 

What is the Hall Effect?

The Hall Effect, also called the Hall–Heroult effect, is the influence of the transverse component of an electric current on the magnetic field in a transverse Hall bar. When a current flows in a plane perpendicular to the direction of the magnetic field, the Lorentz force acts on the magnetic charges (magnetic flux) enclosed by the transverse current. 

The Lorentz force is the force experienced by a magnetic charge when acted upon by an external force field, which in this case is the transverse electric current. Since the electric current has a certain polarity, the Lorentz force pushes the enclosed magnetic charge into a direction parallel to the electric current.

This motion of the magnetic charge produces a magnetic field that is perpendicular to the current, and by Faraday’s law, the resultant Lorentz force produces a tangential magnetic field. Thus, the Hall effect is also referred to as the transverse Hall–Heroult effect.

The Hall voltage generated in a magnetic field is called a Hall effect. In physics, a Hall voltage is a voltage generated when current flows perpendicular to a magnetic field. It is proportional to the current density, hence inversely proportional to the sample thickness (the Hall effect does not work with planar devices).

History

The Hall Effect was discovered independently in 1890 by Orest Chwolson and Edwin Powell in the U.S. and in Russia by Vladimir I. Vernadsky. Edwin Powell and Orest Chwolson reported their findings of the Hall effect in Nature in October 1890, where they described the effect as ‘Hall’s Law.’ 

But the term Hall effect was first suggested by Orest Chwolson, who used the term Hall law in a paper published in 1892. The paper was not well received by the Physical Society in New York, due to the unorthodox terminology that Chwolson had used. After further investigation by E.M. Purcell and Joseph Henry, a second paper by Chwolson was accepted by the Physical Society, and the terminology Hall Effect was used.

 

Theory 

The Hall Effect can be defined by two variables:

• The electric current through a current-carrying conductor (the input).

• The magnetic field surrounding the conductor (the input) and one observable variable the Hall voltage that develops across a Hall plate (the output).

Magnetic Field 

In the Hall Effect, an electric current passes through a current-carrying conductor. The magnetic field surrounding the conductor is inversely proportional to the radius of the conductor. The current through the conductor can be thought of as two fluxes (current flowing in opposite directions) in quadrature; the product of the fluxes gives the total flux through the conductor.

If the conductor is thin and the total flux is very small, the magnetic field around the conductor is approximately uniform. This gives an approximate formula for the magnetic field, that when multiplied by a constant, produces the Hall voltage measured across the conductor

Voltage 

When an electric current passes through a conductor, it produces an electrostatic field around the conductor due to the electrical charges of the current. The charges of the current produce a potential difference across the conductor. If the conductor is made up of one or more conductors with currents in the same direction, it is a common case that a Hall voltage develops across the conductor, and is measured as the output. 

Electromagnetic Effect 

The Hall Effect is an electromagnetic phenomenon, and it can be applied to many electromagnetic devices. This is because the current-carrying conductor, the Hall plate, and the magnetic field all have an electrical charge and produce an electric field in the space surrounding them. For example, a magnet produces a magnetic field, and when a current of electrons passes through the magnetic field, the electrons change direction and produce an electric field in the surrounding space. 

Electronic Effect 

When electrons pass through the conductor, the movement of electrons produces a voltage between the electrons and the conductor. This is because they are all negative, and if they were charged in a similar way to a battery, they would repel each other and form a positive space between them and the conductor.

 

The voltage that is produced by this is proportional to the current through the conductor. This current can be obtained by measuring the Hall voltage and applying the formula.

 

What are the Applications of Hall Effect? 

Understanding this concept in its initial level involves an explanation of the scope of practical application that Hall effect derivation has. These are as follows:

• Hall effect helps in measuring the magnetic field around an electrical charge, and thus qualifies as a magnetometer. 

• Hall effect formula enables one to determine whether a material serves as a semiconductor or an insulator. 

Hall effect definition finds immense application in integrated circuits (ICs) in the form of Hall effect sensors.

The Hall devices are used to measure the current and potential in a circuit. This is useful in many applications such as in integrated circuit design and testing. Common implementations include high-side and low-side Hall devices.

These are small solid-state semiconductor devices used to measure magnetic fields, such as those produced by Earth’s magnetic field, and used in a number of other applications, such as sensing for vehicles, aerospace and electronic devices. Hall sensors are also a popular alternative to reed switches for use in small appliances such as microwave ovens, microwave bread toasters and cordless vacuum cleaners.

In the metallic conductor, electrons are free to move from one point to another. Due to this freedom of movement, the conductor can be polarized by the magnetic field. The movement of electrons causes a change in the resistance of the conductor which can be measured by a Hall voltmeter. This change in resistance is dependent on the direction and strength of the electric field. In this effect, the resistivity of the conductor changes and the magnitude of resistance changes with the direction and the strength of the magnetic field.

The ability of the Hall Effect to measure the electric field enables its application in measuring the resistivity and the surface conductivity of non-metallic materials. Metallic materials do not have the magn
etic field to induce an electromotive force but metallic wires can have current flowing through them.

The magnitude of the voltage is proportional to the strength of the electric field, and hence this enables the development of high-resolution Hall voltmeters.

With a brief light shed on its applications, let us move on to how you can make the Hall effect derivation from scratch.

How to Make Hall Effect Derivation? 

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Hall effect physics involves a metal body that contains a single form of charge carriers, like electrons. Also, the metal warrants a lack of movement of charges along the y-axis.

Therefore, one has to consider the following components of Hall effect expression components to have a better understanding of the derivation – 

 

However, the ‘I’ component within the Hall effect calculation stands for –nevA. In this case, ‘I’ stands for an electric current, ‘n’ signifies the number of electrons per unit volume, and ‘A’ is the conductor’s cross-sectional area. 

Therefore, the Hall effect derivation refers to the following – 

[eE_{H}Bevfrac{evH}{d}=BevV_{H}=Bvd]

However, this derivation stipulates that the force is downward facing because of the magnetic field (equal to the upward electric force), in the case of equilibrium. 

Another way to find the exact value of VH is through the following equation – 

[V_{H}=frac{-Bi}{net} frac{EH}{JB}=-frac{1}{ne}]

This particular equation takes the help of Hall effect coefficient derivation, which is – 

[frac{EH}{JB}]

Besides, the Hall coefficient (RH) implies the ratio between the product of current density and magnetic field and the induced electric field. 

However, the derivation of RH takes into account the factors as stated below – 

Therefore,

[R_{H}=-frac{1}{ne}mu=frac{v}{E}=frac{J}{neE}=sigma R_{H}=frac{RH}{rho}(v)]

Also, you should be aware of the fact that the Hall angle in the Hall effect stands for the angle between electric field and drift velocity. It is essentially the ratio between density (signified by the x-axis) and current density (denoted by the y-axis). 

Hall resistance or [R=frac{VH}{i}-frac{B}{net}]

The hertz which has the symbol: Hz is the derived unit of frequency in the International System of Units that is known as the SI and is defined as one cycle per second. It is said to be named after Heinrich Rudolf Hertz. 

Scientist Heinrich Rudolf Hertz was a German physicist who first conclusively proved the existence of the waves which are electromagnetic and this was predicted by James Clerk Maxwell’s equations of electromagnetism. The unit that is of frequency is the cycle per second was named “hertz” in his honour.

Here, we are going to discover a few more things about the topic.

Why is Hertz Used?

In the field of physics. hertz which is often denoted by the symbol ‘Hz’ can be defined as the derived unit of frequency. We can say this as per the International System of Units. It is an important thing to note that frequencies are often expressed in multiples of Hertz which is such as kilohertz that is denoted by kHz, megahertz denoted by MHz, gigahertz is denoted by GHz. The SI Unit based on the unit of the Hertz is second-1 or we can say that s-1. We need to notice that the Hertz is an SI derived unit.

In English, we can say that “hertz” is also used as the plural form. MHz is the megahertz or 106 Hz. Similarly, GHz that is gigahertz is 109 Hz and THz or terahertz is 1012 Hz.100 Hz means “one hundred cycles per second”, and so on. The unit usually may be applied to any event which is periodic— for example, we can say that a clock might be said to tick at 1 Hz or we can say that a human heart might be said to beat at 1.2 Hz.

Hertz as Unit of Frequency

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency which emphasizes the contrast to the frequency that is the spatial and angular frequency. We can say that frequency is measured in hertz that is denoted by Hz which is equal to one occurrence of a repeating event per second. 

The period is said to be the duration of time of one cycle in a repeating event so the period is said to be the reciprocal of the frequency. For example, we can say that if a newborn baby’s heart beats at a frequency of 120 times a minute then it is 2 hertz is its period denoted by the letter T,  the time interval which is between beats is half a second that is said to be 60 seconds divided by 120 beats. 

Hertz Applications

Frequency is an important parameter that is used in science and engineering to specify the rate of oscillation and the phenomenon of vibratory vibrations such as mechanical vibrations of the audio signals or the sound radio waves and light.

The frequency of any phenomenon can be expressed in hertz but we can say that the term is used most frequently in connection with alternating currents which are electric and the waves which are electromagnetic such as light, radar, etc and sound as well. It is said to be a part of the International System of Units based on the metric system. The unit was adopted in October 1933 by a committee of the International Commission of Electrotechnical and is in widespread use today that is said to be although it has not entirely replaced the expression which is the cycles per second.

An older method that is of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is said to be intense repetitively flashing the light that is strobe light whose frequency can be adjusted with a calibrated timing circuit. 

Let’s suppose that the water has to be transferred from one tank to another. The energy/push given for the water supply is the potential difference and the measure of the same is done by a voltmeter.

If the waterfalls in minute drops (small electric current), then this water flow is measured by a galvanometer. 

The conversion of galvanometer into voltmeter is done by adding a highly-resistive multiplier in series. 

Galvanometer to Voltmeter Formula

We know that for the conversion of a galvanometer into a voltmeter, a high resistance is required. So, if the resistance of the galvanometer is G and that of the high resistance is R, when they are connected in series, the total resistance of the arrangement becomes the following:

     RSeries    =   G + R    

Now, the galvanometer behaves as a voltmeter. How does this happen? Now, we will look at the same thing in the form of the following experiment.        

Galvanometer to Voltmeter Conversion Experiment

We all know that the potential difference applied across the ends of a conductor is a voltmeter. We can convert the galvanometer into a voltmeter if we know its resistance and the figure of merit.

Now, let’s perform an experiment to determine the readings we encounter while doing the conversion of galvanometer into voltmeter:

The Objective of the Experiment:

To Convert the Given Galvanometer of Known Resistance and Figure of Merit into a Voltmeter of Desired Range and to Verify the same Experiment.

Apparatus Required for this Experiment:

The following are the instruments required to perform the conversion of galvanometer into voltmeter:

• A galvanometer

• Voltmeter of 0-to-3 V

• A source: battery

• Two one way keys

• Two resistance box, one of 10,000 ohms and another of 200 ohms

• Rheostat: A variable resistor

• Connection wires

• A sandpaper

The formula for the series resistance required for the conversion is:

                   R = V/Ig – G

Procedure for the Conversion of a Galvanometer into a Voltmeter:

• Connect the resistance box in a series combination across the galvanometer and then collect the plugs of resistance R.

• In the above diagram, A and B are the fixed ends/terminals and C is the variable terminal of the rheostat (a variable resistor).

• We can see that the galvanometer works as a voltmeter under the range of V Volts.

• Now, take out the plugs of calculated resistance R from the resistance box.

• Now, use the key to adjust the movable contact of the rheostat such that the deflection of the galvanometer reaches the maximum ranger.

• Note the readings of both the galvanometer and voltmeter.

• Convert the readings of the galvanometer into V or volts.

• Check if there is a difference in the reading and this difference between voltmeter reading and galvanometer reading may show an error.

• Now, by moving the variable contact of a rheostat, take six readings covering the range of voltmeters from 0-to-3 V.

Observation of the above Experiment:

Conversion of Galvanometer into Voltmeter Practical Observations

Calculation part:

Here, 

The resistance of the galvanometer is = 

The current for a full-scale deflection is = I

Number of divisions on the given galvanometer scale is = n

The figure of merit of galvanometer formula is:

Ig  = nk or k = Ig/n,is the required figure of merit of galvanometer formula.

The resistance in series to be calculated will be used in the following formula:

R = V/Ig – G                        

The final result of the experiment:

We found that there is a minute difference in the value of the actual and the measured one and the conversion is seemingly perfect.

Conversion of Galvanometer into Ammeter Practical Observations

For the conversion of a galvanometer into an ammeter of range ‘I’, we require a shunt resistance and it can be calculated by the following formula:

                               S = (Ig * G)/(I – Ig)

Where,

S = shunt resistance

Ig = nk  is the needed full-scale deflection of a galvanometer. The unit of the figure of merit of a galvanometer is amp/div.

I = A range of the desired ammeter in mA

The length of the wire required to create a shunt is calculated by:

I = π[^{r^{2}}]  S/ρ

Where,

r = radius of the wire calcula
ted by using a screw gauge. This wire is used for making the shunt 

ρ = the resistivity of the given material wire

Conversion of Galvanometer into Ammeter Practical Observations:

1. The resistance of the galvanometer in …..ohms.

2. The figure of merit in……..ampere per division.

3. A number of divisions in a given galvanometer, n…..

4. The desired range of the current in an ammeter is……milliamperes.

Liquid is one of the states of matter which is an incompressible fluid that doesn’t have its own shape, rather it takes the shape of the containing vessel.

Pressure in Liquids:

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The total normal force (or thrust) exerted by liquid per unit area of the surface in contact with it is called the pressure of liquid.

Let F be the normal force acting on the surface area A in contact with liquid, the pressure exerted by liquid on this surface is given by,

                                              P = F/A

The unit of pressure in SI is NM⁻² or Pascal (denoted by P). 

In cgs system it is dyne cm⁻².

The dimensional formula is [ML⁻¹ T⁻²].

What is Fluid Pressure?

The fluid pressure is the measurement of force per unit area on an object in the fluid or on the surface of a closed container. When the fluid is kept inside the container. The molecules of it start a random motion and collide with each other and with the walls of the container. Due to this, they suffer the change in momentum, and also transfer some momentum to the walls.

This in turn generates a force on the walls of the container.

Pressure in Fluids:

The pressure in fluids can be caused by gravity, acceleration, or by forces outside a 

closed vessel. Since a fluid spreads completely in the container. Therefore, it exerts pressure in all directions.

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Consider a point A in the fluid inside a container as shown in Fig.2. 

Just imagine a small area ΔS containing the point A. 

Let the common magnitude of forces be F. 

So the pressure exerted by the fluid at point A is given by,

      

For a homogeneous fluid, this quantity doesn’t depend on the orientation of ΔS .

So, the pressure of fluid at point A is a scalar quantity having only magnitude.

Experiment to understand hydrostatic pressure and fluid pressure

Consider a bottle having water in the form of layers inside it.

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If we look at this bottle, the water is filled in layers, where the layer 1 is the topmost layer, layer-2, the middle one and the lowest layer-3.

The layer 1 doesn’t carry the weight of the other two layers of liquid.    

Layer-2 carries the weight of layer-1, and layer-3 carries the weight of both the layers above it.

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When I make a hole in the point corresponding to each layer, the strongest stream of water comes out from the lowest layer.                                                                        

 

So, here we can say that the lowest layer has the highest pressure while the upper layer has less pressure.

Therefore, the fluid at rest comes into motion and the pressure exerted by it on the base and the walls of the container increases with depth. 

Hydrostatic Pressure and Fluid Pressure

In fluid mechanics, for any fluid at rest, the study of the pressure in a fluid, at a given depth is called the hydrostatic pressure.

Mathematical Proof:

1. Vertical Container

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Let us consider two points A and B separated by a small vertical height dz. 

A small horizontal area as ΔS₁ with a A and an identical area ΔS₂ with point B.

Here, ΔS = ΔS₁ =  ΔS₂ .

Now, consider two surfaces with areas ΔS₁ and ΔS₂ and thin vertical boundary joining them.

Let 

F₁ = Vertically upward force acted by the fluid below it.

F₂ = Vertically downward force acted by the fluid above it. 

W1 = Weight acting vertically downwards.

Let the pressure at the surface A = P 

The pressure at B = P + dP.

Then, by the formula P = F.A we have:

                           F₁ = P ΔS 

and,                    F₂ = (P + dP) ΔS

Then volume of the fluid becomes (ΔS)(dz).

If the density of fluid at A is ρ.

Then mass of the fluid  = ρ(ΔS.dz) and weight is given by,

                        W = mg = ρ(ΔS.dz) . g

For vertical equilibrium,

                             F₁  = F₂  = W

                             PΔS = (P + dP)ΔS = ρ(ΔS.dz) . g

                             On solving it gives,

                             dP = – ρgdz…..(1)

As we move up through a height dz, the pressure decreases by ρgdz.

Now consider a point z =0 at P₁ and another one z = h at P₂ .

Integrating eq(1)

[int_{P_{1}}^{P_{2}} dP] = –  [int_{0}^{z} rho g dz]

P₂  –  P₁ =  – ρgz – 0

                    

If the density is same everywhere then, 

                      P₁  = P₂ = – ρgz …..(2)

2. Horizontal Container

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Now, we would consider a horizontal container having a pressure P₁ at point A in area ΔS and pressure P₂  at point B in the same area ΔS.

Where  ΔS₁ = ΔS₂ = ΔS

 If the fluid remains in equilibrium, the forces acting in the direction AB will be:

                            P₁ ΔS =  P₂ ΔS

                             Or    P₁ = P₂   

Hence, the pressure is the same at two points in the same horizontal level.

What are Infra-Red Radiations?

The infrared radiation wavelength ranges between 700 nanometers and one millimeter. They have a longer wavelength than visible light and have a frequency of about 300 to 400 GHz.

The infrared radiation definition is crucial in understanding related concepts and its applications as well. Hence, students should note here that infrared radiations are not visible to the naked eye. Instead, they can only be felt by a human in the form of heat. 

Although infrared rays have specific properties similar to that of light rays, they are not the same. Features like polarising, reflection, etc. can be observed with infrared radiations.

What are the Uses of Infrared Radiations?

Before delving into the infrared radiation uses, students should be clear about a vital aspect. Infrared radiations are put into applications in two forms – rays and waves. The sources of infrared radiation and visible light are the heat or thermal rays. 

In broad terms, it is the sun and fire that are the prime sources of infrared radiations. 

However, they are trapped and used in multiple areas, including medical applications.

• The other applications include infrared radiation uses in physical therapy. It warms the body and helps in muscle relaxation. 

• The rays are also used in photography. Usually, digital cameras use this technique to click images. 

Out of all these applications, the infrared radiation therapy in both muscle relaxations and medical areas have gained immense significance. It is also hoped that the recent advancements will lead to further areas of applications.  

So, after reading the above lesson, students should also be able to answer the following questions. Give it a try for yourself and assess your knowledge.

Test Your Learning So Far

Fill in the blanks

1. Infrared radiations have a wavelength higher than …………. nm.

2. The visible spectrum has a wavelength ……….… than infrared radiation.

3. X-rays have a wavelength ………….. than infrared radiation.

4. ………… radiations are also called thermal waves.

5. Infrared rays have a wavelength nearing …….…. Hz.

Answers: 700, longer, shorter, Infrared, 300 to 400

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