AP Physics 1 & 2 Wave Characteristics

Hi everyone and welcome back to Educator.com.0000

I am Dan Fullerton, and today we are going to start our study of waves by talking about wave characteristics.0002

Our objectives are going to include defining a pulse and describing its behavior at a boundary, describing waves using the term speed, wavelength, frequency and amplitude, explaining characteristics of transverse and longitudinal waves, understanding the basic nature of sound waves...0008

...and finally utilizing the wave equation to analyze behavior of waves in a single medium.0024

Number 1 -- Waves transfer energy and they transfer energy through matter or space.0033

A lot of different types of waves -- things like sound waves, light waves, microwaves, radio waves, water waves, seismic waves, slinky waves, x-rays, even the waves at the stadium when the waves are going around the stadium when you are at a ball game.0039

A lot of different types of waves and they all transfer energy.0055

Now as we start talking about waves, let us start with a single disturbance.0061

A single disturbance which carries energy through a medium or through space is known as a pulse, and over here we have a picture of a pulse.0065

Imagine that you have a string tied to a wall and you send one pulse down the string.0071

A wave then is a series of pulses, a repeated disturbance which carries that energy.0077

The pulse in this case, for a string, you see that it has a displacement that is vertical but it is traveling horizontally.0082

There are also waves where the displacement will be in the same direction as the wave's velocity.0090

Now when a pulse reaches a hard boundary, something like a wall, it is going to reflect off that boundary, but when it does it is going to come back inverted.0096

If this pulse were going against a hard wall -- let us draw our pulse here -- and it is traveling to the right -- and there is our wall, it is attached to a solid object.0104

Once it hits that wall, what it is going to do is it is going to come back, but as it does that it is going to be inverted.0114

On the other hand, if it reaches a soft or a flexible boundary, imagine for example that you have it tied to a ring around a pulse so that the end can go up or down, well then when it reflects off a boundary, it is not going to invert.0124

In that case, you are going to have something kind of like this.0138

The waves traveling toward a stop -- in this case this is free to move up and down -- you have a loose or flexible boundary, so when this one reflects, it is actually going to come back without being inverted.0141

So pulses at boundaries -- you can have inverted reflection or non-inverted reflection.0158

And there are bunches of types of waves.0165

We are going to break them up in several different ways, but the first way we are going to break them up is whether they are a mechanical wave or an electromagnetic wave.0166

The key difference is that mechanical waves require a medium to travel through or some sort of matter to travel through.0174

Water waves travel through water, sound waves travel through air, slinky waves are traveling through the slinky, and seismic waves in the earth travel through the earth; they all need a medium through which to travel.0181

Electromagnetic waves on the other hand do not require a medium -- the only type of wave that can travel through a vacuum.0194

Light waves, radio waves, microwaves, x-rays are all different forms of the electromagnetic spectrum or sometimes we refer to them as different forms of light, but really light is just a small portion of the electromagnetic spectrum, the portion that our eyes can perceive.0201

So types of waves motion -- waves in which the displacement of the medium is in the same direction as the wave velocity are known as longitudinal or compressional waves.0216

If the displacement of the medium is going side to side and the wave velocity is in the same direction, that is a longitudinal wave.0225

The most common example here is a sound wave.0234

As I am talking to you right now, that sound wave is a compression of air -- the air molecules are moving back and forth, vibrating, and they are coming toward you.0238

The velocity is in the same direction as the wave disturbance -- a longitudinal wave, sometimes known as a compressional wave.0248

Waves in which the displacement of the medium is perpendicular to the wave's direction of motion are known as transverse waves, and these are a little bit easier to visualize because that is where you start to see this sort of pattern.0258

If we have this wave traveling to the right, the disturbance of the medium -- notice that it is traveling up and down, perpendicular to the direction of wave velocity -- that is a transverse wave.0269

Things like seismic S waves, stadium waves and electromagnetic waves even, but note that electromagnetic waves, even though they do not have a medium, the electric fields and the magnetic fields in an electromagnetic wave are traveling perpendicular to the direction of the wave's velocity.0282

Now light gravity and the electric force, the effects of light, sound and other radiating phenomena all follow that same inverse square law relationship -- the same thing that we have been studying comes up again, and again, and again in nature and therefore in physics.0301

Let us take a look at a transverse wave in a little bit more depth. A lot of different pieces that we can label here -- vocabulary terms.0319

First off, crest is the peak point and the trough is the low point.0325

The amplitude is the displacement from the equilibrium to a crest or to a trough; it is related or corresponds to the wave's energy, and one wavelength is the distance from crest to crest, trough to trough, or the same point on consecutive waves.0330

For example that point there to that point there would also be one wavelength.0349

Now simple waves are typically described by sine and cosine functions.0355

The form x = A cos(ωT), which we have studied before, and if that is a little bit unfamiliar, now would be a great time to take a quick break and go review this simple harmonic motion lecture.0360

Now another thing we want to point out here is what is called the phase angle.0374

Points on the same wave with the same displacement from equilibrium moving in the same direction are said to be in phase.0377

For example, that point there on that wave front and that point there -- those points would be in phase.0384

If they are not in phase, let us say 180 degrees out of phase, would be exactly between those two -- half a wavelength between those.0391

If we wanted to look at points that were out of phase, a really easy one to do -- let us take a point there and that point there -- those are in phase.0399

What would be out of phase with those two?0407

That point right there would be 180 degrees out of phase with those two other solid red dots, so in phase versus out of phase.0410

First example problem -- Which type of wave requires a material medium through which to travel?0420

Our choices are sound, television, radio and x-ray.0427

Well, if it requires a material medium, that is what we call a mechanical wave.0430

The mechanical wave here is sound -- it has to travel through air; sound is vibrating air molecules, so sound is the mechanical wave.0437

Television, radio and x-ray -- all of those are electromagnetic waves and none of those require a medium through which to travel; they can all travel through a vacuum.0445

Let us take a look at the direction of displacement.0457

The diagram below shows a transverse wave traveling to the right through a medium.0461

Point A here represents a particle of the medium.0465

In which direction will particle (A) move in the next instant of time?0468

Well the key here is if it is a transverse wave, the direction of the particles of the medium must be perpendicular to the velocity, so it can be moving up or down in this diagram.0472

You can think it is almost as if you have a rider on the wave.0484

The whole wave is moving past (A), but (A) cannot move to the left or right; it is a transverse wave.0487

As the wave velocity goes to the right, this whole sine-cosine function is going to move to the right.0493

(A) -- the first thing it is going to do is it is going to slide down as this wave passes it to the right, so the correct answer would be 'down'.0501

The other way you can solve these, if you really want to know how to do them quickly -- imagine if the wave velocity is traveling to the right, instead imagine the wave is standing still and the particle is moving in the opposite direction, so it would be going down the hill, again, down is the direction.0509

A ringing bell is located in a chamber.0527

When the air is removed from the chamber, why can the bell be seen vibrating but it cannot be heard?0530

Well light waves can travel through a vacuum but sound waves cannot; there is our answer right there.0536

Electromagnetic waves can travel through there without any air in the chamber, so you can have that information get to your eyes through the chamber, but you are not going to get any sound waves because there is nothing for the sound to travel through.0543

Sound is a mechanical wave; it requires air, a medium.0555

If there is no medium, you do not get any sound.0558

Let us take a look now in a little bit more detail at longitudinal waves.0563

Longitudinal waves, sometimes called compressional waves, have areas of compression where you have many, many particles, high density and areas of very low density known as rarefactions.0567

Now the wavelength can still be found by going from compression to compression, or rarefaction to rarefaction.0577

But in this diagram, the particles are going to be vibrating back and forth in that plane and the wave velocity is going to be in that same direction.0584

That is what makes it a longitudinal wave.0594

A periodic wave is produced by a vibrating tuning fork.0599

The amplitude of the wave would be greater if the tuning fork were -- well remember amplitude relates to the energy of the wave, so the amplitude would be greater if -- well, that is going to happen if we strike it harder, it is going to be louder, it corresponds to the energy when struck harder.0603

How about amplitude of a sound wave here?0624

Increasing the amplitude of a sound wave produces a sound with...?0627

Lower speed -- No, amplitude does not have anything to do with speed.0630

Higher pitch? No. Shorter wavelength? No.0634

Greater loudness? Again, amplitude refers to energy and loudness is going to correspond to energy in a sound wave.0637

Let us talk about some more characteristics of wave -- frequency and period and we have talked about these briefly in mechanics as well.0647

The frequency of a wave describes the number of waves that pass a given point in a time period of 1 second.0654

The units are going to be 1/s or Hertz.0659

Higher frequencies mean you have more waves per second.0663

On the other hand, period (T) describes how long it takes for a single wave to pass a given point and those units are just in seconds.0667

As we have discussed previously, frequency is 1 over the period or period is 1 over the frequency.0676

What is the period of a 60 Hz electromagnetic wave traveling at 3 × 10⁸ m/s?0685

We are given its frequency (60 Hz), which is also equal to 60 (1/s) and we want to know the period.0692

Well period is 1 over frequency, so that is going to be 1/60 (1/s), or about 0.0167 s, which is pretty straightforward.0703

What is the product of a wave's frequency in its period?0721

We are going to multiply frequency times period.0725

If we do this, remember that frequency is equal to 1 over period, so I am going to replace frequency with 1 over period.0730

We still have it multiplied by the period so I get period divided by period or 1.0738

Again, we are just exploring that inverse relationship.0747

Now let us talk about the wave equation.0752

The velocity of a wave is a function of the type of wave and the medium it travels through.0755

Now electromagnetic waves moving through a vacuum have a speed of 3 × 10⁸ m/s.0761

All electromagnetic waves moving through a vacuum have this speed.0767

That is so important that it actually gets its own symbol -- (c) is the speed of an electromagnetic wave in a vacuum (3 × 10⁸ m/s).0770

We are not going to have anything go faster than that.0779

Electromagnetic waves moving from vacuum to a different medium can slow down.0783

If the wave re-emerges back into a vacuum, it is going to return to its original speed.0788

Now the speed of the wave is related to its frequency and its wavelength, and for a given wave speed, as frequency increases, wavelength decreases and vice versa; this is known as the wave equation: V = F(λ).0792

Now the key here as we look at this is understanding that this is a relationship; it is not implying causality.0806

As the wave changes media, the frequency is what is going to remain constant -- the speed can change, the wavelength can change, but the frequency of the wave is going to stay the same as it enters a new media.0813

If it slows down -- a wave slows down as it goes into a new medium, its wavelength is going to have to decrease because frequency remains constant.0825

Let us see how we can apply this.0835

A periodic wave having a frequency of 5 Hz, -- frequency is 5 Hz and a speed of 10 m/s has a wavelength of...0837

... Well, let us apply our wave equation V = F(λ), which implies then that wavelength equals V/F or 10 m/s/5 Hz or 5 (1/seconds) is just going to be 2 m.0851

Or the period of an electromagnetic wave -- An electromagnetic wave traveling through a vacuum -- right away when I know it is traveling through a vacuum, I know its velocity is 3 × 10⁸ m/s -- has a wavelength of 1.5, so wavelength λ is 1.5 × 10^-1 m.0876

What is the period of this electromagnetic wave?0897

We are trying to find period, but I do not know how to find period from velocity and wavelength, but I could use the wave equation to find frequency, so let us start there.0900

If V = F(λ), then that means frequency equals velocity over wavelength or 3 × 10⁸ m/s divided by the wavelength λ, which is going to be 1.5 × 10^-1...0910

...but oh, by the way, frequency is 1 over period, so that is going to be 1 over the period.0930

If I want just the period then, the period is going to be 1.5 × 10^-1 m/3 × 10⁸ m/s...0934

...and that is going to come out to be about 5 × 10^-10 s, or 0.5 nanoseconds.0947

All right. Let us take an example with a blue whale.0963

A surfacing blue whale produces water wave crests having an amplitude of 1.2 m every 0.4 s.0966

If the water wave travels at 4.5 m/s, find the wavelength of the wave.0973

We have an amplitude of 1.2 meters (A = 1.2 m) every 0.4 seconds, so you get a wave crest every 0.4 s, so that must be the period, the time for one complete wave -- T (period) is 0.4 s.0980

The water wave travels at 4.5 m/s, so velocity = 4.5 m/s. Find the wavelength.0998

We will go to our wave equation again: V = F(λ), but we know that frequency is 1 over period, so I could write this as V = λ/T, and if I want λ, the wavelength, then λ = V × T (period).1008

Now I can substitute in my values -- λ = 4.5 m/s (velocity) × 0.4 s (period)...1029

...which will give us a wavelength of about 1.8 m.1039

All right, taking a look here at sound waves.1050

Sound is a mechanical wave that is observed by detecting vibrations in the inner ear.1053

Now typically we think of sound as traveling through air, or the medium is the vibration of air particles, but note that sound can also travel through other media.1057

It can travel through water, through wood, through steel, and it can travel through many other things.1067

You have probably heard a sound wave when you were under water before.1072

Particles of a sound wave vibrate parallel with the direction of the wave's velocity -- it is a longitudinal wave or a compressional wave.1076

Finally, the speed of sound and air at standard temperature and pressure, are sometimes reported a little bit differently in different books but you are right around 343 m/s.1083

That is the value you typically see on the AP exam.1093

At standard temperature and pressure, 343 m/s is the speed of sound.1096

All right, let us take an example with some speakers.1104

At an outdoor physics demonstration, a delay of half a second was observed between the time sound waves left the loud speaker and the time these sound waves reached a student through the air.1107

So we have a speaker over here and we are going to have sound waves traveling until they get to our student -- that time was 0.5 seconds from the speaker to the student.1117

If the air is at standard temperature and pressure, I know the velocity of the wave is going to be 343 m/s.1135

How far was the student from the speaker?1145

We are looking for this distance, so let us call that δx.1147

The way I am going to solve that is I am going to go back to my very basic kinematics.1153

If velocity is change in displacement over time, then our displacement there, δx, is going to be velocity times time, or 343 m/s times; 0.5 s (time).1158

The student must be standing about 172 m from the speaker.1176

All right. Resonance, one of those fun topics in physics.1186

Certain devices create strong sound waves at a single specific frequency.1189

Another object that has that same natural frequency may begin to vibrate at that frequency in a process known as resonance.1194

A classic example of this that you might have seen on TV or different places is an opera singer shattering a crystal glass by singing a high pitch note.1201

As that singer sings that high pitch note with a loud amplitude, if they hit the exact same frequency -- is the natural frequency of that crystal, the crystal may start to vibrate along with it.1210

And if those vibrations, those sympathetic vibrations, those resonant vibrations are strong enough, it can actually shatter the crystal.1221

An example is a car traveling at 70 km/h that accelerates to pass another car.1232

When the car reaches a speed of 90 km/h, the driver hears the glove compartment start to vibrate.1238

I think I had this car; this might have been my first car.1243

You got going just a certain speed and the whole thing started shaking and you thought it was going to come apart and if you went just a little bit faster, all of a sudden everything calmed down again.1246

By the time the speed of the car is 100 km/h, the glove compartment door has stopped vibrating.1255

This vibrating phenomenon is an example of -- that must be a resonance effect.1260

The resonance of the car's vibration along with the car itself when you hit that certain speed causes everything to vibrate.1267

Get going a little bit faster and now all of a sudden the sound waves that are being emitted, all those vibrations are not at the natural frequency of the rest of the car and you do not have that great buildup of energies.1276

Sonar signal problem -- A stationary research ship uses sonar to send a 1.13 × 10³ Hz sound wave...1289

...let us write that down -- frequency (1.18 × 10³ Hz) -- down through the ocean water.1298

The reflected sound wave from the flat ocean bottom, 324 m below the ship is detected at 0.425 seconds after it was sent from the ship.1307

So we have a time of 0.425 s, and how far did that travel? Well, let us think about it.1318

Over here let us draw our ship and I will give it a nice, little mast and flag, whatever it happens to be, and there is the ocean bottom.1324

If it sends a signal down, it bounces off the bottom and comes back up, and in one direction it is 324 m below the ship, so the sound wave must have traveled twice that or 648 m.1333

So our change in -- or the distance traveled here -- δy -- we will call 648 m.1348

Calculate the speed of the sound wave.1356

Well the velocity is δy/T which is going to be 648m/0.425 s or 1525 m/s.1359

Notice now that because we are in water, the velocity of the sound wave is significantly higher.1374

It is no longer 343 m/s like it was in air at standard temperature and pressure.1378

Next question it asks us is to calculate the wavelength of the sound wave.1386

Well let us go back to our wave equation -- if V = F(λ), then λ = V/F, which is going to be 1525 m/s over our frequency (1.18 × 10³ Hz) or about 1.29 m.1392

Part C -- Determine the period of the sound wave in water.1416

Well period is just 1/frequency, so that is going to be 1/1.18 × 10³ Hz or 8.47 × 10^-4 s.1421

Another example -- Waves across media.1446

A light wave travels from vacuum into glass.1449

As it does so -- as it goes from vacuum into glass we know it is going to have to slow down so velocity is going to decrease and the frequency of the wave stays the same.1453

That does not switch when you switch media, so we are going to have the same frequency and what else is going to happen?1464

Well if velocity equals frequency times wavelength and we said frequency must stay the same -- if velocity drops then that means that wavelength must drop as well.1473

So what is our right answer?1484

Its speed decreases and wavelength decreases, so (A) works. How about (B)?1485

Speed decreases -- that is okay -- and its wavelength increases -- no.1490

Speed increases -- no; speed increases -- we can get rid of all of those speed increases.1495

Speed decreases and frequency decreases or increases -- no, frequency stays the same.1501

Its wavelength decreases -- that is true -- and its frequency increases -- no, frequency stays the same, and here we have frequency decreases.1508

So out of all those choices, the only correct answer must be (A), its speed decreases and its wavelength decreases.1515

All right. Let us check out one last sample problem.1524

A piano plays a middle C which has a frequency corresponding to pitch of 256 Hz in air at standard temperature and pressure.1528

We know frequency is 256 Hz and if it is at standard temperature and pressure, then air, sound, velocity must be about 343 m/s.1538

What is the distance between compressions of the sound wave? -- Oh! Tricky.1551

The distance between compressions at the same point on the alternate waves, is going to be the wavelength, so we are looking for λ.1557

We can use our wave equation, V = F(λ).1566

Therefore wavelength is equal to velocity divided by frequency or 343 m/s/256 Hz, therefore wavelength = 1.34 m.1571

Hopefully that gets you a good start on wave characteristics.1595

Thanks so much for your time and attention, and make it a great day.1598