Category: Physics Notes PPT

Lenz’s Law named after the physicist Emil Lenz was formulated in 1834. It states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.

When a current is induced by a magnetic field, then the magnetic field produced by the induced current will create its magnetic field. Thus, this magnetic field will be opposed by the magnetic field that created it. 

Lenz’s law is based on Faraday’s law of Induction which says, a changing magnetic field will induce a current in a conductor whereas Lenz’s law tells us the direction of the induced current, which opposes the initial changing magnetic field which produced it. Hence, this is signified in the formula for Faraday’s law by the negative sign.

[ epsilon = -frac{dPhi _{B}}{dt}]

The magnetic field can be changed by changing its strength or by either moving the magnet towards or away from the coil, or moving the coil in or out of the magnetic field.

Hence we can say that the magnitude of the electromagnetic field induced in the circuit is proportional to the rate of change of flux.

[ epsilon alpha  frac{dPhi _{B}}{dt}]

Lenz Law Formula:

According to Lenz’s law, when an electromagnetic field is generated by a change in magnetic flux, the polarity of the induced electromagnetic field produces an induced current whose magnetic field opposes the initial changing magnetic field which produced it.

The formula for Lenz law is shown below:

[ epsilon = -N(frac{dPhi _{B}}{dt})]

Where,

[ epsilon ] = induced EMF

[dPhi _{B}]  =  change in magnetic flux

N = number of turns in the coil

Lenz law applications:

The Applications of Lenz’s Law Include:

When a source of an electromagnetic field is connected across an inductor, a current starts flowing through it. The back electromagnetic field will oppose this increase in current through the inductor. To establish the flow of current, the external source of the electromagnetic field has to do some work for overcoming this opposition.

1. Lenz’s law is used in electromagnetic brakes and induction cooktops.

2. It is also applied to electric generators, AC generators.

3. Eddy Current Balances

4. Metal detectors

5. Eddy current dynamometers

6. Braking systems on train

7. Card Readers

8. Microphones

Lenz Law Experiment:

To find the direction of the induced electromotive force and current we use Lenz’s law. Some experiments are below.

First Experiment:

In the first experiment, when the current in the coil flows in the circuit, the magnetic field lines are produced. As the current flows through the coil increases, the magnetic flux will increase. The direction of the flow of induced current would be such that it opposes when the magnetic flux increases.

Second Experiment:

In the second experiment, when the current-carrying coil is wound on an iron rod with its left end behaving as N-pole and is moved towards the coil S, an induced current will be produced.

Third Experiment:

In the third experiment, the coil is pulled towards the magnetic flux, the coil linked it goes on decreasing which means that the area of the coil inside the magnetic field decreases. 

According to Lenz’s law, the motion of the coil is opposed when the induced current is applied in the same direction.

To produce current, force is exerted by the magnet in the loop. To oppose the change a force must be exerted by the current on the magnet.

An example of Lenz Law:

In a copper or aluminum pipe, there is the presence of large magnetic fields that cause counter-rotating currents. Dropping the magnet through the pipe demonstrates this particular phenomenon. When the magnet is being dropped within the pipe it tends to descend at a rate that is lower than when it is dropped outside the pipe. Here there is a current induced which can be determined using the right-hand rule.

Let us assume that you are reading a book sitting on your sofa,  now,  think whether you are in motion or at rest? Clearly,  here you are at rest. But let us try to re-evaluate the situation. We all live on this earth that is continuously moving,   so now,  are you in the state of motion or at rest? Well,   finding answers to this complex question can be slightly confusing but let us break down the concepts and  simply learn about  motion and its types.

Whenever we speak about motion or rest it is always explained with reference to some fixed point which is known as the origin. So,   with respect to the change in the position,   we have two quantities that can be used to describe any change in the position and they are distance and displacement. The distance can be defined as the total path covered during the motion. It can be represented by a magnitude only. While displacement can be defined as the shortest distance between the initial and final position. It requires both the magnitude and direction for complete representation.

Our daily activities including walking,   running,   etc. involve linear movement. There is a change in the position of the object involved in these activities. 

Some Examples of Motion are: 

Fish swimming in the water,    dropping of stone from a certain height,   the flow of air which is coming in and out of our lungs,   the automobiles carrying passengers from one place of pick up to the destination is also an example of motion. As we can notice that different objects move in different ways. Some objects move in a curved path while some in a straight path and a few others in a zig-zag way. Depending on the path taken by the particle the motion can be classified as projectile motion,   rectilinear motion,   rotational motion,   and many more. In this topic,   we have discussed the linear motion definition. Let’s understand more about classification.

With respect to the nature of the movement,   motion is classified into three types as follows: 

• Linear Motion

• Rotary Motion

• Oscillatory Motion

What is Motion?

Motion is the free movement of a body with respect to time. It can be defined as a process of changing position. For example-a moving train,  a rotating fan,   a ball rolling around etc. Even though this universe is in continuous motion,   but,   there are different types of motion which will make your understanding more detailed and clear.

With respect to the nature of movement,  motion is mainly categorized into four different types:

1. Rotatory Motion – this is a kind of motion in which the object rotates around a fixed axis. For example,  a rotating fan.

2. Oscillatory Motion – in oscillatory motion an object repeats in the same motion continuously back and forth. For example,  a pendulum.

3. Linear Motion – this motion is a one dimensional motion that takes place in a straight line. For example,  a train running on a track.

4. Reciprocating Motion – this motion is a continuous up and down or back and forth motion. For example,   a gymnast swinging on a ring.

Linear motion meaning the change of position of an object with respect to time interval. We live in a universe that is in continuous motion. The fundamental particle of a matter i.e.,   atom is also in constant motion. Every physical process happening in the universe is composed of some sort of motion. The motion can either be fast or slow,   but motion always exists.  Motion is described in terms of the following terms: Distance,   Displacement,   Speed,   and Time as discussed above.

In general,   a body will be said to be in motion if it changes its position with respect to a reference point and time. While describing the Linear Motion we require only one coordinate axis along with time to describe the motion of a particle then it is said to be in linear motion or rectilinear motion. In linear motion,   the particles will move from one point to another point either in a straight line or a curved path. Basically,   in linear motion an object travels the same distance at the same time and the object can move in a straight or a curved path from one point to another. 

Depending on the path of motion linear motion is further subdivided as: 

• Rectilinear Motion – It is a path of motion in a straight line. In this motion all particles travel the same distance following a parallel straight line.

• Curvilinear Motion – It is a path of motion in a curved line. The orientation of the body in space does not change, but the trajectories of individual particles of the body are curved.

Types of Linear Motion:

• Uniform Motion – a body said to be in uniform motion when it moves in a straight line at a constant speed. For example a car moving at a steady speed on a straight road. In a graphical representation uniform motion can be represented by a straight line.

• Non-Uniform Motion – a body covers and equal distances in a set and given time intervals it is said to be in non uniform motion. In the graphical representation this motion can be represented as a curved line.

An object is in a linear motion if the object moves in a straight line,   on the other hand,   an object is in a rectilinear motion if two objects move in a straight line and are parallel to each other. The two types of linear motion are uniform motion and non-uniform motion but the three types of rectilinear motion are uniform rectilinear motion,   uniformly accelerated rectilinear motion and rectilinear movement with non-uniform acceleration.

Rotatory Motion

In the above topic,   we have discussed linear movement definition,   rotary motion is the type of motion occurring when a body rotates on its own axis. The most common example of rotatory motion is the Spinning wheel and the motion of the earth around the sun about its own axis.When we drive a car,   the motion of wheels and the steering wheel about its own axis is also considered as Rotary motion.

Oscillatory Motion

We have discussed what linear motion is,   let’s know about Oscillatory motion. It is the type of motion in which a body moves around its mean position. Some examples of oscillatory motion are: The pendulum of a clock is in oscillatory motion as it moves to and fro about its mean position. The string of the guitar when strummed also moves to and fro about its mean position which results in an oscillatory motion.

Conclusion

In this article,   we have discussed Motion and different types of motion are also discussed. Types of Linear motion along with Rotary motion and Oscillatory motion are also described. Below are some examples to have a clear understanding of uniform motion and nonuniform motion.

Eg: If a car is travelin
g at a speed of 50 km/hour then it will cover a distance of 1 km/minute. In this sense,   the motion of car acceleration is uniform. A boy after kicking a football. It may cover 5 meters in the first attempt,   10 meters in the second change,   6 meters in the third attempt,   and so on as per the velocity exerted by the boy.

MCB is the acronym used for the miniature circuit breaker and is commonly used in our day to day lives. Its primary function is to break the circuit when the current flowing through the circuit reaches past a certain set limit. In conditions such as short circuit or overload, these devices trip by themselves hence saving the house by the damages caused by a short circuit or overload or as the case may be. The mechanism of MCB has 3 possible positions, ‘ON’, ‘OFF’, and ‘TRIPPED’, hence the breaker provides manual means of opening and closing of the circuit. MCB is a kind of a better version of a fuse.

MCB Symbol

MCB Electrical

MCBs work on a time-delay tripping mechanism. This means that they function whenever there is an overload or higher flow of current for a longer duration of time, the duration which can hamper the normal functioning of the circuit. The time duration if exceeds a certain value the MCB trips and breaks the circuit thus rendering the overload dysfunctional in damaging the appliances and further circuit. 

What is MCCB?

MCCB is the short form for a moulded case circuit breaker. It is used to protect the electric circuit from the flowing of excessive current which can further cause damages such as overload and short circuit. They are being used for a wide range of frequencies with the current rating up to 2500A and adjustable trip settings. MCCB provides overload protection via the temperature-sensitive component. These are usually used in PV systems in place of miniature circuit breakers. These work on principles of electromagnetism and cam also be disconnected manually. MCCB’s are subjected to high current, therefore they need proper maintenance and can be maintained by regular cleaning, lubricating, and testing.

How is MCCB different from MCB?

MCB’s trip characteristics may not be adjusted since they are mostly provided to low circuits with the MCB rated 100 amps with an interrupting rating of under 18000 amps. Whereas MCCB has the characteristics of the adjustable trip which is used in higher models. MCCBs provide amps between 2500-10 and their interrupting rating ranges from 10,000 amps to 200,00 amps. Hence this states that MCB is usually used for low energy requirements such as home wiring or small electric circuits, on the other hand, MCCB is more suited for high energy requirements.

MCB being rated under 100 amps doesn’t come with the feature of the adjustable trip, hence they always cater low current circuit.  Whereas MCCBs being rated from 10 to 2500 amps comes with an adjustable trip feature so they can cater for high current circuits

Although an MCCB possesses a higher capacity than an MCB, both are classified under low voltage circuit breakers and should respond to standards set by the IEC 947. For the sake of convenience, MCCB is equipped with a special feature of being tripped only by remote as their units have electrical motor operators. Whereas MCB lacks this feature.

MCCB is said to be more suited for higher energy due to the possession of better capacity than MCB, whereas MCB is usually provided for low energy requirements, hence they are best suited for them.

Obviously, when it comes to home use or some light work, the MCB is better preferred due to low energy requirements. On the other hand, when it comes to industrial use or any other heavy-duty requirements, MCCB is the best suited.  

Difference Between MCB and MCCB.

Did You Know?!

The miniature circuit breaker was invented by Stotz-Kontakt, a company that was established in Mannheim, Germany, in the year 1891.

For designing a magnetic levitation project in class 12, you’d first need to understand the concept of maglev, otherwise known as the magnetic levitation. In the magnetic levitation device, we’ll be designing a demo of the moving maglev train without wheels. The trains would hover on the tracks because of the magnetic levitation and would remain suspended in the air because of the magnetic field generated. For the train’s movement, the generated magnetic field can pull on nearby magnets (based on their poles) and, thus, create a force that pushes the train.

What is Magnetic Levitation?

It’s compelling and simple science that works to get objects levitated and known to humanity for more than a century. Here, an object that is suspended mid-air with no additional support except magnetic fields observes movement in them. The magnetic fields reverse or counteract the gravitational pull and other forces acting on the body. 

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As the magnetic fields begin interacting with the metallic loops of aluminum present in both ends of the concrete walls, it creates a magnetic field strong enough to push the train forward. Since the train gets pushed and causes movement, an electric current is generated and further triggers the creation of successive magnetic fields. 

It can be understood in three main principles:

• Mag-lev Principle: These metallic loops or coils resemble figure 8, and as the superconducting magnets pass at high speeds, the coils generate an electric current. The forces acting on the superconductor magnet push it upwards in a robust and counteracting magnitude, thus levitating the train.

• Lateral Guidance: As the running maglev system is displaced laterally, the loop generates a current that is present under the tracks. Thus, there is a creation of a repulsive force acting near the train’s side, while there’s an attractive force acting further apart from the train, causing it to maintain a central position. 

• Electromagnetic Propulsion: The repulsive and attractive force pushes the train forwards. The coils present on both the sides of the walls act as propulsion coils, which are also charged by the three-phase alternating current. 

Materials Required 

For our magnetic levitation project, we need: 

1. Magnetic tape with a width of 0.5 inches, and cut into two 24 inches units and two 5 inches units

2. Two, Perpendicular plastic angle pieces – each 24 inches long and 3/4th inches wide

3. A woodblock with the dimensions of 5 x 3/4 x 1 or 1/2 inches as length, breadth, and height respectively

4. Either a flat piece of wood or corrugated cardboard –  24 inches long and 3 inches wide.

5. Transparent, double-sided tape

6. Scissors

7. Plastic cup or paper

8. Coins

9. Ruler

10. Kitchen scale for measuring

Please note that the materials’ above dimensions would help you design the project according to the model we are using as a reference. You can also opt for different equipment sizes, but in that case, you’d require to adjust the spacing between the tracks and the other components of the project. 

Step-By-Step Procedure

• Step I: Begin with peeling the paper off the short magnetic strips and attach them to one side of the wooden block aligned completely with its edges. This shall be the block of your train model. In case you don’t have a magnetic strip with sticky ends, you can always stick it with transparent, double-sided tape. (Take reference from the figure below.)

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Draw a centerline down the middle of the base.

Draw one line from 5mm distance on both sides of the centerline.

Draw one line from a 20mm distance on both sides of the centerline.

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• Step IV: Once the lines are drawn, stick the long metallic strips and plastic angle pieces to the bases at aligned spaces, crucial for its working.

1. First, place the long magnetic strips at least 10mm apart from each other in a way that their inside edges are aligned with the lines 5mm from the centerline.

2. Using the double-sided tape, stick the plastic angle pieces in a way that their inside edges align with the lines 20mm from the centerline, and are at 40mm apart. 

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Data Collection

• You can now collect crucial data for knowing how much weight your magnetic levitation project can handle. You’d require a table that shall record the mass and distance it travels. As a standard unit of measure, use grams for mass and distance in mm. 

• The first recorded value should begin with no mass (or zero mass). Calculate the distance between the train and the track, taken from the top of the magnet strips on the track and the bottom of the magnet strips of the train model. 

• Place a plastic cup with a few coins in it, and observe if the train model remains parallel to the tracks. If it gets tilted, you can always shift the plastic cup to balance the train.

In physics, the relationship between mass and energy in a rest frame of the system is the mass-energy equivalence, in which two values can only be different by the unit of measurement and a constant. 

Mass-energy equivalence implies that, even though the total mass of a system changes, the total energy and momentum remain constant. Consider the collision of an electron and a proton. It destroys the mass of both particles but generates a large amount of energy in the form of photons. The discovery of mass-energy equivalence proved crucial to the development of theories of atomic fusion and fission reactions.

Einstein’s Mass-Energy Relation

Mass-energy equivalence states that every object possesses certain energy even in a stationary position. A stationary body does not have kinetic energy. It only possesses potential energy and probable chemical and thermal energy. 

According to the field of applied mechanics, the sum of all these energies is smaller than the product of the mass of the object and the square of the speed of light.

When an object is at rest when it is not moving and shows no momentum, the mass, and energy results are equivalent and they can only be differentiated by one constant, that is, the square of the speed of the light (c2). 

Mass-energy equivalence means mass and energy are the same and can be converted into each other. Einstein put this idea forth but he was not the first to bring this into the light. He described the relationship between mass and energy accurately using his theory of relativity. The equation is known as Einstein’s mass-energy equation and is expressed as,

E=mc2

Where E= equivalent kinetic energy of the object,

m= mass of the object (Kg) and

c= speed of light (approximately = 3 x 108 m/s)

The formula states that a particle’s energy (e) in its rest state is the product of mass (m) with the square of the speed of light,c. 

It is because of the large numbers of the speed of light in everyday units. The formula says that the rest mass of a small amount resembles a large amount of energy even though it’s independent in the making of the matter. 

Let’s go deep into the topic and understand what is rest mass? 

Rest Mass

The mass that is calculated while the system is at rest is known as Rest mass, which is also known as invariant mass. 

It is a physical property that is not dependent on momentum, even when it’s approaching the speed of light at high speeds. 

The invariant mass of Photons which are massless particles is zero while free particles which are massless consist of both energy and momentum. 

The SI units of energy (E) are calculated in joules, mass (m) is calculated in kilograms, and speed of light ‘c’ is calculated in meters per second. 

Derivation of Einstein’s Equation

Derivation I

The simplest method to derive Einstein’s mass-energy equation is as follows,

Consider an object moving at a speed approximately of the speed of light.

A uniform force is acting on it. Due to the applied force, energy and momentum are induced in it.

As the force is constant, the increase in momentum of the object= mass x velocity of the body.

We know,

Energy gained= Force x Distance through which force acts

E= F x c ………………………………………… (1)

Also,

The momentum gained = force x Duration through which force acts

As, momentum = mass x velocity,

The momentum gained = m x c

Hence, Force= m x c ……………………………. (2)

Combining the equation (1) and (2) we get,

E= m c2

Derivation II

Whenever an object is in speed, it seems to get heavier. The following equation gives the increase in mass due to speed.

$m = frac{m_0}{sqrt{frac{(1-v^2 }{c^2}}}$

Where,

m- the mass of the object at the traveling speed

m₀– the mass of the object at a stationary position

v- speed of the object

c- speed of the light

We know, in motion, an object possesses kinetic energy and it is given by

E= ½ (mv2)

Total energy possessed by the object is approximately equal to kinetic energy and increases in mass due to speed. 

E≅ (mc2) + ½ (mv2)

E- (mc2) = ½ (mv2)   , for small v/c

E= Relativistic kinetic energy + mc2

The relativistic kinetic energy depends on the kinetic energy and speed of the object. We can simplify the equation by setting the speed of the object as zero. Hence the equations become as follows,

E= 0+mc2

E= mc2

Applications of Einstein’s Equation

The first person to put forth the word that the mass and energy’s equivalence as one of the general principles and the outcome of symmetry of time and space was Einstein. Einstein’s theory was used to understand nuclear fission and fusion reactions. Using the formula, it was revealed that a large amount of energy is liberated during nuclear fission and fusion processes. This phenomenon is used in creating nuclear power and nuclear weapons.

To find out binding energy in an atomic nucleus, the equation is used. By measuring the masses of various nuclei and subtracting them from the sum of masses of protons and neutrons, Binding energy is calculated. Measurement of binding energy is used to calculate the energy released during nuclear reactions. 

These energies seem much smaller as compared to the mass of the object that is multiplied by the square of the speed of the light. Because of this principle, atoms after a nuclear reaction have less mass than the atoms before the nuclear reaction. The difference in the before and after mass shapes up as heat and light with the same energy used as the difference. 

Einstein’s equation is used to find out the change in mass during the chemical reactions. Whenever there is a chemical reaction, breakage and the formation of new bonds take place. During the exchange of molecules, a change in mass takes place. For chemical energy, Einstein’s equation can be written as 

E= Δm x c2

Where Δm- change in mass

The formula provided by Einstein can be written with E as the energy which is released and removed and m can be written as the change in mass. 

It is explained in relativity, all the energy that an object moves with, provides a contribution to the total mass of that body, which is used in measuring how much it can resist accelerating. 

When the observer is at rest, the removal of energy is the same as the removal of mass which goes by the formula m = e/ c2. 

The radioactivity of various elements is based on the theory of mass-energy equivalence. Radioactivity produces X-rays, gamma rays. So in many radiotherapy equipment, the same principle is used. 

To understand the effect of gravity on all-stars, moon, and planet, and to measure the age of fossil fuels.

In many surgeries, where opening and stitching of body parts is not done, Cath lab is used. It works on Einstein’s equation.

To understand the universe, its constituents, and the age of planets, The equation is used.

The word “acoustic” is related to sound or the sense of hearing. It is a branch of sound that deals with understudies of mechanical waves in solids, liquids, and gases. These mechanical waves can be of sound, vibrations, ultrasound, and infrasound.

Since we are dealing with sound waves, so we will talk about Acoustic Sound. Sound travelling in the form of waves has some speed that can be in m/s, kmph, and mph. 

Speed of sound is the distance travelled by a unit wave through the air/elastic medium carrying various units of measurement. 

On this page, you will find multiple units of sound with the experiment to measure speed of sound in air.

Important Point:

In the 17th century, the French scientist and philosopher Pierre Gassendi is known to be the dist to attempt the measuring the speed of sound in air.

Speed of Sound in Air

For measuring the speed of sound, we need to measure the distance it covers through the medium.

For instance, the speed of sound in meters per second (in dry air) is 343 meters per second; however, this velocity value is considered at a temperature of 20 ⁰C (68 ⁰F).

Moving forward, the speed of sound is measurable in various media and units like we discussed for m/s (m/s = SI unit of speed).

Now, let’s discuss the speed of sound in miles per hour, speed of sound km per hour,  and how the experiment for the determination of the speed of sound can be performed:

Speed of Sound in Various Units

The speed of sound is measured in the following units:

• Speed of sound in Km per hour      –     1,235 Kmph

• Speed of Sound in miles per hour   –      767 mph

• Speed of sound in air feet per second      –      1,125 ft s⁻¹

The velocity of sound is measured in hydrogen and oxygen (H2 and O2) is always 332 m/s.

Before starting with the experiment to measure the speed of sound, we must know the sound measurements symbols:

Measuring the Speed of Sound in Air

Point to Note:

The speed of sound strongly depends on the temperature and the medium through which it propagates.

Do You Know the Speed of Sound is Measured by Which Instrument?

We can measure the speed of sound by using an oscilloscope, a square-wave oscillator, and a piezo-electric pick-up. 

A study of the connection between the space travelled, and therefore, the time of arrival of the sound wave allows a graphical determination of the speed of the heartbeat within the lucite rod.

Now, let us understand the experiment to measure speed of sound in air:

Experiment to Determine the Speed of Sound

Theory 

In 1866, August Kundt first described this experiment. In this context, we will be performing a common experiment in physics. The acoustic tube is also known as the Kundt’s tube.

Aim of this Experiment:

This experiment aims to measure the speed of sound “c” in air, or other gasses, by observing standing acoustic waves in a tube. 

 

Do You Know?

We can determine the speed of sound in the air by using a smartphone and a cardboard tube.

However, for making the experiment economical/affordable in terms of equipment. We are measuring the speed of sound within 3% of the theoretical prediction.

Theory of the Experiment:

Now, start with the theoretical part:

We place the smartphone such the microphone is found within the opening of the tube. this is shown in the figure below:

The phone is about to record audio with a frequency of 44.1 kHz. During the phone recording, the function generator app emits a pure wave. 

The wave traverses a path from 50 Hz to 3000 Hz at a rate of 1 Hz s−1. The sound recording is stored in .wave format. This format makes for straightforward data analysis later.

For a sinusoidal wave with constant frequency f  and wavelength, propagating in a medium, the speed of sound in the said medium is given by:

           c  =   fλ

On determining the wave’s frequency and wavelength, we can measure the speed of sound in the medium. 

When an acoustic wave enters through the open end of a half-closed tube and hits the closed-end, part of the wave is reflected towards the tube’s opened end. At specific wavelengths, the incident and the reflected wave form a standing wave. 

In the antinodes of the standing wave, the points on the standing wave where the amplitude is maximum, the amplitude of the standing wave is greater than the amplitude of the incident wave.

The displacement antinode of the standing waves is the opening of the tube. The resonance wavelengths are the wavelengths at which the standing waves occur.

For the half-closed tube, the resonances occur when the tube’s length equals an odd number of quarter wavelengths of the incident wave:

                       λn  = 4L/n,  

Where

  n  =  1, 3, 5,….

Here,

“n” is the nth harmonic of the tube

L is the length of the tube.

The resonance frequencies fn of the tube, the frequencies at which standing waves occur in the tube, can be found by combining both equations:

                                λn  = 4cL/n, 

Where

n  =  1, 3, 5,…..

Result:

Frequencies at peak amplitudes: