Wave equation = Pure Awesomeness + Mind Blown

Quote of awesomeness: “Teacher who make Physics boring are criminals” ~ Walter Lewin

This is truly mind-blowing, eye-popping, jaw-dropping and hair-splitting stuff.

Isn’t physics such a surprising and interesting subject? I mean, yeah, it can get hard to a moment where you just don’t want to do it, but if learned properly, physics is amazing and can be used in so many different ways in our daily lives. We will dive deeper into this, like…. hm… right now!

Let’s start with wave equations! 

Wave Equations

Okay, for example, we are given a couple of questions on finding the wavelength, the velocity, or the frequency of a wave. Yes, yes, it does actually sound a bit intimidating at the beginning but it’s OKAY you’ll do awesome after we learn more about it? Ready? Okay, great, let’s start learning for real now. Most of the time, the problem given would have the details of either the wavelength, the velocity, or the frequency (the details shown with the problem you will be solving will really depend on which one [the frequency, wavelength, or velocity] they are asking you to solve.). The wavelength depends on 2 things:

  1. Frequency
  2. Wave speed

Shall we try it out?

you can do it. i really know it.

Before we start with a problem, let’s substitute everything.

Let’s work it out like this:

V = Velocity

F = Frequency

λ = Wavelength

[Cool (greek) Note: You may be wondering like “What the what?!?!!? What is λ???”. Same, that’s exactly how I first thought about it. But, it’s actually a Greek letter (the 11th letter of the Greek alphabet, to be exact!) which is known as Lambda. Greek letters can often be seen used in science and in math. The λ in physics is used mostly with wavelength, btw, just like we will be doing here. If you search up “what does λ mean in physics?”, you’ll mostly scan the page with the word wavelength in them! Cool, huh?]

Finding the Wavelength, λ

First problem equation for finding the wavelength (A.K.A, the λ).

Word Problem 1: What is the wavelength of a sound wave moving at 340 m/s with a frequency of 256 Hz?

Step 1, we will first have to see what we are given already in problem 1. As we reread the question, we will come across two given numbers, 340 m/s, and 256 Hz. Now, it is time to reveal the identity of these numbers so that we will be able to solve the equation. 

340 m/s is the velocity

256 Hz is the frequency

Step 2, since we finished finding what we have already and identifying each of the numbers given, we will now write the equation down and solve it! We will start with the equation

V = λ * F 

[Here’s a reminder of what each symbol means:

Velocity = Wavelength * Frequency]

Since in problem 1, the question is asking for the wavelength, we will have to change the equation a bit, here’s how we will do it:

V = λ * F

[Divide both sides by F(requency) so that we can get wavelength alone]

V/F = λ * F/F

[When we divide both sides by F, we cancel out the F/F (which is frequency/frequency) And, then, the equations turns into this: ]

V/F = λ  [let’s just switch it around so that it’s easier to look at]

=

λ = V/F, this is our equation for wavelength. 

In case you are still a bit confused about the symbols and what they mean, the final equation above is actually this:

λ = V/F means Wavelength = Velocity/Frequency

The next thing to do is plug in the numbers in the equation. Remember that we were given(?):

340 m/s is the velocity

256 Hz is the frequency

When we put it into our equation it should look like this —–>

λ = 340/256, 

You can just go ahead and grab your calculators for this, the answer should be

λ = 1.328 m/s

Answer: The wavelength of this sound wave is 1.328 m/s.

Aaaaand, you got you wavelength! That wasn’t so bad, right? We’ll do another equation but quicker this time and then we will move onto our next thing!

Second problem equation for finding the wavelength (A.K.A, the λ).

Word Problem 2: The rightmost key on a piano produces a sound wave that has a frequency of 4185 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength.

We have the frequency, 4185 Hz, and we have the assumed speed or velocity, 343 m/s, now all we have to do is finish the equation.

V = λ * F   [divide both sides to get wavelength]

V/F = λ * F/F   [the F/F gets canceled out and we successfully just have wavelength by itself]

λ = V/F   [now we have the Wavelength = Velocity/Frequency]

λ = 343/4185   [here, we plugged in the numbers we already have then we just have to divide it]

λ = 0.0819 m/s   [now, we’ve got our wavelength: 0.0819!]

Answer: The wavelength of this equation is 0.0819 m/s.

Yayyy!! You were able to find out the wavelength of an equation but before we continue with frequencies and velocity, here’s the question: “What is a wavelength?”. A wavelength is the length of a single wave cycle. Here’s a picture —->

wavelength

Here is the measure of a single cycle, it is the horizontal line with the double-sided arrow.

Remember, the λ = wavelength here.

 

Finding the Frequency, F

First problem equation for finding the Frequency.

Word Problem 1: The light waves from a laser pointer have a wavelength of 670nm and travel at 300Mm/s. What is the frequency of the oscillating source of these waves?

We are given the information:

670nm which is the wavelength

300Mm/s is the velocity

Now, we are being asked about the frequency. Let’s first write down:

V = λ * F 

Since we want to get the frequency this time, we will be diving both sides by λ (wavelength):

V/λ = λ/λ * F

The λ/λ will then cancel out and you will be left with this equation:

F = V/λ 

Time to plug in the numbers we have! Remember(!): 670nm is the given wavelength, whereas, 300Mm/s is given as the velocity. 

F = 300/670 

Once you’ve divided the numbers, we will get the answer of:

F = 0.4 cycles/seconds

Answer: The frequency of the oscillating source of these waves is 0.4 cycles/seconds.

There you got the Frequency! Let’s move on to solving the velocity.

Finding the Velocity, V

First problem equation for finding the Velocity.

Word Problem 1: Ocean waves 12m in length strike a seawall with a frequency of 0.5 Hz. How fast do these waves move?

So, we have the 12m, the wavelength λ, and 0.5 Hz, the frequency F.

Remember how we always start with the equation: V = λ * F? Now, we don’t have to change the equation for finding the Velocity as the equation is already made to do that exact thing! Let’s get into the calculations.

V = 12 * 0.5 

[let’s do the math]

Answer: These waves move 6m/s.

Let’s do another word problem on velocity, this one will be really easy, I promise.

Second problem equation for finding the Velocity.

Word Problem 2: A wave had a frequency of 14 Hz and a wavelength of 3 meters. How fast is the wave moving?

Oh, you probably already have the answer, you’re doing great!

V = 3 * 14 = 42

The wave is moving 42 m/s




 

 

You did a great job and I hope you had a fun time!!

 

Yours truly,

L.O.A.S.H

 

 

 

 

 

 

 

 

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