Wave Speed

Summary

Highlights

• Light travels faster than sound, which is why you see lightning before hearing thunder. ⚡️
• Wave speed is calculated by dividing wavelength (Lambda) by the period. 🔢
• Simulations show how tension and medium affect wave speed. 🔍
• Increasing tension in a medium increases the wave speed. 💨
• Everyday examples, like sound in different materials, help illustrate these concepts. 🎵

Key Takeaways

• Wave speed is determined by the medium it travels through. 🌊
• Wavelength and frequency have an inverse relationship when the medium is constant. 🔄
• Tension affects wave speed - more tension means faster waves! 💥
• Practical examples like thunderstorms help illustrate wave dynamics. ⛈️
• Wave speed can be calculated using both wavelength and frequency or distance and time. 📏⏰

Overview

Chapters

• 00:00 - 00:30: Introduction to Wave Speed This chapter introduces the concept of wave speed, emphasizing the difference in arrival times of light and sound waves. The example of a thunderstorm is used to illustrate how light reaches an observer faster than sound, highlighting the concept of wave speed. As a thunderstorm approaches, the gap between the arrival of light and sound decreases, demonstrating the principles of wave speed in real-world scenarios.
• 00:30 - 01:00: Wave Speed Calculation The chapter focuses on the concept of wave speed calculation. It starts by describing how waves transfer energy through oscillations and then delves into the definition of speed in the context of waves. Speed is described as the distance traveled over a given period of time. The text explains that for waves, distance is measured as wavelength (often represented by the Greek letter lambda), and time is measured as the period. The chapter concludes by showing that dividing the wavelength by the period gives the calculation for wave speed.
• 01:00 - 01:30: Wave Speed and Medium The speed of a wave is influenced by the medium through which it travels. Sound waves, for example, travel faster in water compared to air. This relationship is quantified by the wave velocity, which can be calculated using the equation V = λ/T, where λ is the wavelength and T is the time period. Additionally, since frequency is the inverse of the time period, the formula for wave speed is often expressed as V = λ * f.
• 01:30 - 02:00: Wave Speed Simulation The chapter discusses the relationship between wave speed, wavelength (Lambda), and frequency, explaining that wave speed is the product of wavelength and frequency. It introduces a simulation where wave behaviors can be visually analyzed. Through this simulation, the effects of tension and the damping medium on wave speed can be examined. Changes in tension and the damping factor affect wave speed, and the simulation demonstrates how adjusting these parameters can vary wave speed.
• 02:00 - 02:30: Calculating Wave Speed Experimentally The chapter titled 'Calculating Wave Speed Experimentally' describes an experiment to calculate the speed of a wave. A wave is sent down a medium, and its progress is measured. The wave is stopped at a distance of 6 cm, and it took 1.6 seconds for the wave to travel that distance. The chapter emphasizes calculating wave speed by using the basic formula: speed = distance/time.
• 02:30 - 03:00: Effect of Tension on Wave Speed The chapter discusses how tension affects wave speed and explains that wave speed can be observed and calculated by different methods. Initially, the wave speed of 0.38 m/s is noted based on observation. Additionally, the formula for velocity using wavelength (Lambda) and frequency is mentioned to calculate wave speed. The wavelength is suggested to be around 2.5 cm according to the simulation.
• 03:00 - 03:30: Speed of Sound in Different Mediums The chapter discusses how the speed of sound is determined by frequency and wavelength, highlighting that velocity can be calculated if both are known. An example is given with a wavelength of 0.25 meters and a frequency of 1.5 Hertz, resulting in a speed of 0.38 meters per second. The chapter also explores how altering the properties of the material through which sound travels can affect its speed, noting an increase in speed with increased tension.
• 03:30 - 04:00: Relationship Between Wavelength and Frequency The chapter discusses the relationship between wavelength and frequency, using an example of calculating the velocity of a wave based on time and distance covered. When the tension increases, the speed also increases. The formula V = Lambda F is used, where Lambda represents the wavelength and F represents the frequency, which is given as 1.5 in the example.
• 04:00 - 05:00: Example Problems and Conclusion The chapter discusses the relationship between tension and wave speed, demonstrating how reducing tension decreases speed significantly. It also compares the speed of sound in different materials, noting that sound travels at 331 m/s in air, faster in water, and even faster in steel.

Wave Speed Transcription

• 00:00 - 00:30 [Music] hi it's Mr Anderson and this is AP Physics Essentials video 107 it's on wave speed if you spent any time in a thunderstorm you know that the Light reaches you much quicker than the sound does and so if it's far away there will be a big gap in those two waves arrival time but as it gets closer and closer and closer the time between those two waves arriving the light and then the
• 00:30 - 01:00 Thunder is going to get closer and closer and closer okay that was pretty close and so waves transfer energy through oscillations since we're talking about wave speed what is a speed remember it's a distance we travel over a given period of time now how do we measure distance when it comes to waves that's going to be the wavelength or Lambda how do we measure time when it comes to waves that's going to be the period so if we simply divide the wavelength by the period we've now calculated the wave
• 01:00 - 01:30 speed now the wave speed is going to depend on the medium uh in other words what it's in for example sound's going to go much faster in water than it does in air so the medium determines that but there's an established relationship between the velocity of the wave and then the Lambda divided by time or the the Lambda divided by the period now lots of times since since the frequency is the reciprocal of the period of time and so instead of being written like that it'll be written like this V equals
• 01:30 - 02:00 Lambda F in other words the velocity or the speed of the wave is the Lambda or the wavelength times the frequency and so let's take a look at that wave speed for a second and so we'll just do this qualitatively so what I'm going to do is start some waves in this simulation and then I'm going to play around with a tension and watch what happens as I make it less tense and then more tense I could also affect how much of it is being dampened by the medium itself and so you can see that I can play around with the medium itself and I can vary the speed of the Waves so let's just
• 02:00 - 02:30 look at one for a second so we're going to keep that tension the same but we're sending one wave down and we'll stop it right when it gets to 6 cm and so now we've watched the wave move so we're going to try to calculate wave speed in a couple of different ways so it's moved a set distance from here to here and again I had the clock running so it took 1.6 seconds for it to make it there and so if I want to figure out its wave speed one way to do it was simply measure distance divided by time so what's the distance in this case we move
• 02:30 - 03:00 060 m per 1.6 seconds you can see I converted that to meters and so what's going to be the wave speed just watching the wave go it's going to be around 038 m/s now we also know that you could calculate it in a different way and so velocity equals Lambda time frequency and so we could calculate Lambda Lambda is going to be the wavelength so let's figure out what the wavelength is so from here to here it's one to like 2.5 cm and also on the simulation it's
• 03:00 - 03:30 telling us what the frequency is and so if I know the frequency and I know the wavelength I know the velocity and let's make sure that that matches so my wavelength is 025 M my frequency is 1.5 Hertz and so it's going to be 038 m/s so same thing we could then CH try to change the makeup of the the uh material or the matter through which the wave is moving so let's start it now so we've increased tension so it went fast fter
• 03:30 - 04:00 you can see the time is less so it's 96 seconds so we could calculate the distance we moved again that's 6 060 m per .96 seconds so that's one way so we could get a velocity that's fast it's much faster than it was before so as we increase tension we've increased the speed but we could also use V equals Lambda F and so what is our Lambda what's our wavelength it's going to be that distance and what's our frequency 1.5 and so we could say it's going to be the same same value and so those are two
• 04:00 - 04:30 ways we could calculate the speed of the wave now what happens if we totally decrease the tension there's no tension inside there oh you can see that it's going really really slow and so I'm not going to keep going on this one it take forever and so as we increase the tension inside the material you can see we're increasing the speed so here's some speed of sound so this is an air 331 m/s in water it's much faster and in steel if you were to just hit steel and then listen to it really far down it's
• 04:30 - 05:00 going to go way faster than it would inside the air itself now let's say we keep the medium the same let's say we keep the tension in everything the same what's going to be the relationship between the wavelength and the frequency of the wave and so let's just start it going and what I'm going to do is vary the frequency and so as I increase frequency what happens to the wavelength you can see it decreases as I now decrease frequency what's happening to the wavelength now you can see the wavelength is increasing so again the medium determines the speed of the wave but then there's this
• 05:00 - 05:30 relationship between the wavelength and the frequency lots of times you'll be given problems like this so for example we're giving this picture you can see the distance between the waves is 23 M we know the velocity of the waves is 2.8 m/ second so could you calculate the wave frequency so here's my equation so V equals Lambda F I plug in what I know in this case I know the velocity and I know the wavelength and I could solve for a frequency of 0.12 Hertz or you could try this problem now I'm giving you the period let's say it's 3.5
• 05:30 - 06:00 seconds you're watching it and that's how much time it takes for the for the boat to move up and down and you could also measure the wavelength and so could you calculate wave speed well give it a try and then include your answer in the video descriptions down below and so did you learn to design an experiment to determine the relationship between the wave speed the wavelength the frequency and relate those to Everyday examples like lightning I hope so and I hope that was helpful [Music]
• 06:00 - 06:30 h