BTEC Applied Science: Unit 1 Physics Waves on a String

Summary

The video by BTEC Applied Science Help focuses on explaining the concept of waves on a string, particularly in musical instruments like guitars and violins. The video elaborates on the differences and relations between transverse and longitudinal waves, explains the concept of stationary waves, and the role of harmonics in sound production. It also walks through detailed examples of calculating wavelengths, frequencies, and the velocity of waves using physics equations, emphasizing principles like tension, mass per unit length, and their impact on wave properties. The video is aimed at guiding students through understanding these foundational physics concepts using practical and relatable examples.

Highlights

• Transverse waves travel perpendicular to their oscillations. 🔄
• Stationary waves are formed by interference of reflected waves. 🚦
• Fundamental frequency relates to string length and creates the base musical note. 🎵

Key Takeaways

• Waves on a string create both transverse and longitudinal waves. 🎸
• Understanding harmonics enriches the musical experience. 🎶
• Calculating wave properties requires understanding tension and string mass. 📏

Overview

In this illuminating session, the video creator keenly dives into understanding waves on strings using relatable examples like violin and guitar strings. The importance of transverse and longitudinal waves is broken down with clarity, making sense of their roles in creating sound.

Explaining stationary waves, the concept of harmonics is introduced. These harmonics, while usually unnoticed, are what give musical instruments their unique sound. This is where physics beautifully intersects with music, providing a basis for the delightful tones we hear.

The tutorial meticulously steps through calculations for wave velocity, wavelength, and frequency, applying physics laws effectively. This structured approach ensures viewers grasp the vital connections between tension, mass per unit length, and their ultimate impact on how we perceive sound waves.

Chapters

• 00:00 - 00:30: Introduction to Waves on a String The chapter 'Introduction to Waves on a String' begins with a focus on waves as applied in the context of strings, which are relevant for instruments like violins and guitars. The instructor notes that while some prior videos have addressed stationary waves and associated equations, students still have difficulty with the topic. As a result, the chapter intends to delve deeper to enhance understanding.
• 00:30 - 01:00: Types of Waves on a String The chapter introduces the concept of waves on a string, specifically using the example of plucking a guitar string to create sound. It identifies two primary types of waves that are generated: transverse waves and another unspecified type. The emphasis is on transverse waves, where it's noted that these waves travel up and down the string, and their oscillations are perpendicular to the wave’s direction.
• 01:00 - 01:30: Wave Reflection and Interference The chapter titled 'Wave Reflection and Interference' discusses the behavior of waves traveling through different mediums. When a wave travels in a medium like a string, it causes vibrations, producing sound which is a longitudinal wave. The chapter emphasizes that although these longitudinal sound waves share the same frequency, their wavelengths differ, which can be a common source of confusion for students. The chapter likely further explores how different wavelengths interact during wave reflection and interference.
• 01:30 - 02:00: Stationary Waves and Harmonics The chapter titled 'Stationary Waves and Harmonics' explains the phenomenon of transverse waves produced when a string is plucked. Initially, these waves travel along the string. Upon reaching the end of the string, they reflect back, contributing to the formation of stationary waves. The discussion sets the stage for exploring the concepts of harmonics as a result of these reflective wave behaviors.
• 02:00 - 02:30: Nodes and Antinodes The chapter titled 'Nodes and Antinodes' delves into the concept of stationary waves that result from waves reflecting and interfering with each other. During this process, the string vibrates in loops, forming a pattern of nodes and antinodes. The chapter emphasizes understanding these loops and the unique properties of stationary waves.
• 02:30 - 03:00: Fundamental Frequency and Harmonics Explained The chapter explains the concept of how a string vibrates to produce sound. The lowest frequency of vibration, which forms a single loop, is called the fundamental frequency or the first harmonic in physics. It mentions a difference in terminology in music where the first harmonic is considered differently.
• 03:00 - 03:30: Wavelength Calculation Example This chapter explains the concept of harmonics in wave physics, focusing on the fundamental frequency, also known as the first harmonic. The fundamental frequency is described as when the length of the string is equal to half a wavelength. Additionally, the chapter briefly mentions the existence of higher harmonics, such as the second and third harmonics, which occur alongside the fundamental frequency.
• 03:30 - 04:00: Factors Affecting Wave Velocity The chapter discusses the phenomenon of wave velocity and how multiple frequencies and harmonics affect our perception of sound. It explains that although multiple harmonics exist and contribute to the overall tone of an instrument, the human ear primarily perceives or notices the lowest frequency. Other harmonics remain in the background, enhancing the sound's beauty and tone without being distinctly noticeable.
• 04:00 - 04:30: Velocity Equation and Examples The chapter discusses the concept of a fundamental frequency in string vibration, focusing on the formation of nodes and antinodes. A fundamental frequency features a single loop that has a central antinode (point of maximum amplitude) and nodes (points of zero amplitude) at each end of the string. Each loop consists of two nodes and an antinode, illustrating the basic principles of wave behavior in physics.
• 04:30 - 05:00: Wavelength Calculation in Fundamental Mode The chapter explains the concept of harmonic frequencies, specifically focusing on the fundamental frequency, which is described as one loop, the second harmonic as two loops, and the third harmonic as three loops. An example is given with a guitar string 85 centimeters long, prompting a calculation for the wavelength of the waves in the fundamental mode.
• 05:00 - 06:00: Frequency Calculation Example In the chapter titled 'Frequency Calculation Example,' the discussion revolves around the vibration of a string in its fundamental mode. It is explained that for this mode, the length (L) of the string is equal to half the wavelength (lambda/2). The chapter likely covers how the wavelength (lambda) can be calculated or rearranged from the provided equation, given that L equals lambda over two for the fundamental mode or the first harmonic.
• 06:00 - 06:30: Practice Problem The chapter 'Practice Problem' discusses the calculation of a wavelength lambda given the value of L as half of lambda. It walks through the mathematical process showing that if the length of the string l equals 85 cm, then lambda is 170 cm or 1.7 meters. The chapter emphasizes on understanding the process for working out similar calculations.
• 06:30 - 08:00: Solution to Practice Problem The chapter discusses the solution to a practice problem involving the calculation of the frequency of a stationary wave. To find this frequency, one must first determine the velocity of the wave, which is essentially its speed. The text notes that velocity is synonymous with speed in this context. Additionally, it mentions that the velocity of the wave depends on the tension in the string. The chapter suggests converting measurements to meters for consistency.

BTEC Applied Science: Unit 1 Physics Waves on a String Transcription

• 00:00 - 00:30 b-tech applied science unit one physics and i'm going to talk about waves on a string i've already done a video about stationary waves and in one of my videos about equations i've talked about this but students find it difficult so i'm going to spend a bit more time on it waves on a string such as a violin or a guitar string
• 00:30 - 01:00 now when i pluck a guitar string guitar string plectrum pluck [Music] two types of waves we get transverse waves which travel up and down the string transverse waves you should remember transverse waves the oscillations are perpendicular to the direction that the wave is
• 01:00 - 01:30 traveling in then the string vibrates and as it vibrates it produces sound which is a longitudinal wave so longitudinal sound waves travel through the air now these two waves they will have the same frequency but they will have different wavelengths and i think this is a problem a lot of students have had is that they get the the two wavelengths modeled up so
• 01:30 - 02:00 i pluck a string [Music] and we are getting transverse waves traveling up and down the string beautiful so the string is plucked transverse waves now what happens is that the waves travel to the end of the string and then they reflect and then we get
• 02:00 - 02:30 interference so we get waves travel in both directions they reflect they come back and they interfere and we get a very special type of wave called a stationary wave a special type of wave called a stationary wave is produced and the string vibrates in a loop think about these loops
• 02:30 - 03:00 okay so the string vibrates up and down like that and the lowest frequency of this vibration is one single loop so the length of the string is one single loop and that's called the fundamental frequency or the first harmonic uh in music the first harmonic is actually somewhere else the first harmonic is there but in physics we say that the
• 03:00 - 03:30 fundamental is the first harmonic and for the first harmonic for the fundamental frequency the length of the string is equal to half a wavelength okay so the lowest frequency is called the fundamental or the first harmonic we actually get lots of other frequencies produced as well we get the second and third etc harmonics but normally we
• 03:30 - 04:00 don't notice them they're in the background our ears just hear that lowest frequency or rather we just notice the lowest frequency but when i play that in the background there's also that and that and that you know the other the other harmonics are there and they make the tone of the instrument they make it sound beautiful but we don't really notice them normally those other harmonics
• 04:00 - 04:30 we notice the fundamental and the fundamental is a single loop in the middle of the string it's vibrating a lot up and down that's called an antinode where the amplitude is maximum and then at the ends of the string where it's not vibrating at all where the amplitude is 0 they're called nodes so each loop is two nodes and an antinode and as i said
• 04:30 - 05:00 i'm repeating myself why not okay the fundamental frequency is one loop the second harmonic is two loops the third harmonic is three loops as i said i've already done a video on that now let's have a look at this simple little question here a guitar string is 85 centimeters long what will be the wavelength of the waves
• 05:00 - 05:30 traveling along the string when it is vibrating in its fundamental mode so you should be able to tell me i will show you now so we said that l equals lambda over 2 for the fundamental mode for the first harmonic l equals lambda over two so lambda rearranging this equation
• 05:30 - 06:00 equals two times the length of the string which will be two times 85 which i believe is 170 centimeters in fact there you go all that out they might see it okay so l is lambda over two lambda equals two times l which is 170 centimeters or 1.7 meters if you're going to work out other stuff
• 06:00 - 06:30 later on be a good idea to change it to meters so now to calculate the frequency of this stationary wave what we would have to do first is work out the velocity of the stationary wave which is how fast it's traveling the speed we call it the velocity velocity speed same thing probably now the velocity depends on the tension in the string and
• 06:30 - 07:00 it depends on the mass per unit length of the string which is basically how heavy it is so the velocity depends on the tension you will notice when i change the tension yeah the frequency changes because the velocity changes so the velocity depends on the tension and it also depends on how heavy
• 07:00 - 07:30 the string is the mass per unit length this string here is a very light string this string is much heavier that's why it's okay you get a different lower frequency because it's heavier it doesn't vibrate as quickly okay so the velocity depends on the tension and the mass per unit length and this is the equation here
• 07:30 - 08:00 v equals root t over mu hopefully you won't have to rearrange it hopefully it will just be a case of working out the velocity but v equals the square root of t over mu t is the tension in newtons mu is the mass per unit length kilograms per meter hopefully you'll be giving it given it in kilograms per meter not grams per meter because then you'd have
• 08:00 - 08:30 to change it to kilograms so t divided by mu and then get the square root v equals v equals root t over mu we'll have a look at a couple of examples of that okay let's have a go at a couple of examples i'll go through this one slowly carefully a violin string has a mass per unit length of naught point naught naught five seven
• 08:30 - 09:00 kilograms per meter now i could have been cruel and said 5.7 grams per meter and then you would have to divide it by a thousand to get kilograms but i've just given you grams per meter sorry kilograms per meter the tension in the string is 49 newtons and its length is 32.5 centimeters calculate the velocity of the waves that travel through the string
• 09:00 - 09:30 calculate the wavelength of these waves when it's in its fundamental mode calculate the frequency that of the sound that these waves will produce so the first thing we're going to work out is the velocity of the waves so v equals root t over mu now you don't need to learn this equation you'll be given this equation in the exam be given all of the equations that you need
• 09:30 - 10:00 you might have to rearrange it to rearrange it you'd have to square both sides to get rid of the square root it'll be a bit fiddly hopefully you won't have to do that you'll just have to work out the velocity fingers crossed so v is for equals root t over mu equals the square root of uh t is 49
• 10:00 - 10:30 and mu is naught point naught naught five seven equals so calculator time so 49 divided by point naught naught five seven equals then square root that equals uh and i've done it wrong do it
• 10:30 - 11:00 again 49 divided by 0.0057 equals square root that equals that's better 92.7 newtons sorry meters per second 92.7 meters per second note to get full marks you need to write down the equation bung in the numbers work it out
• 11:00 - 11:30 one decimal place should do meters per second don't forget the units the wavelength now fundamental mode we remember that the length of the string is half a wavelength so for the fundamental mode the length of the string is lambda over 2 so the wavelength is twice the length so the wavelength will be 2 times 32.5 which will be 65
• 11:30 - 12:00 centimeters which is 0.65 meters now you could leave it at 65 centimeters but the next thing that we're going to do is work out the frequency and to do the frequency we are going to use the wave equation now the wave equation hopefully you remember v equals f lambda is the wave equation
• 12:00 - 12:30 very important and so f is v over lambda which is and we've got v is 92.7 divided by uh 0.65 is the wavelength and we get a frequency of
• 12:30 - 13:00 so 92.7 divided by 0.65 equals 143 hertz don't forget frequencies measured in hertz 143 hertz and that's three sig figs so i'm not gonna bother with the decimal point okay uh here's one for you to have a go
• 13:00 - 13:30 at and i suggest you pause the video and have a go at it okay i'm going to do it now assuming that you've already done it so electric guitar needed a velocity of the waves so i'm just going to zip through it so v is root t over mu equals the square root of
• 13:30 - 14:00 76. divided by dot point naught naught six eight node six eight make my point a bit more obvious equals calculate the time 76 divided by 0.0468 equals square root equals 105 105.7
• 14:00 - 14:30 so 106. three sig figs is enough 106 meters per second okay the wavelength is going to be twice the length so lambda is 2 times l and that will be 2 times that which is 1.3 meters i believe
• 14:30 - 15:00 1.3 meters and then uh again f equals v over lambda f equals b of lambda equals 106 divided by 1.3 equals
• 15:00 - 15:30 81.3 hertz okay so i hope that helped if it did say something nice in the comments uh if it didn't then don't put it do we like okay bye bye for now