SlideShare a Scribd company logo
Beats
From High to Low and
Everything in Between
What are beats?
● When you listen to a song, there are some portions
where you can just hear a *dum dum dum* sound
(*wub wub wub* in other cases), and, more often than
not, we call those the beats of a song.
● 1 *dum*/*wub* = 1 beat
● But what are beats in the first place? And where do
they come from?
Learning Objectives
● Learn how beats are formed.
● Figure out what beats are: physically and
mathematically.
● Visualize why there would be a distinct *dum*
sound for beats
How are beats formed?
● If you have tried plucking two strings of a guitar that
are of different tones, you would have heard a faint
*wub wub* sound. Congratulations! You have just
made a beat!
● When two waves of close frequencies travel together I
the same direction, at any given time, there will be
places that are in-sync, constructively intefering with
each other, places that are out of sync, destructively
interfering with each other, and places in between.
!!!NOTE!!!
● The two waves need to be travelling at the same
direction and have the same amplitude in order to
form a beat.
● They need to have the same amplitude to make a
distinctive beat (one that pinches off to 0)
● They also need to be travelling in the same direction
to be observable. Imagine Listening for two sounds
one coming from the right (entering through the right
ear), and one from the left (entering from the left ear):
there wouldn't be physical interference happening.
What are beats physically?
● If we slowed down that beat, we would hear a
gradual increase from the beat's minimum
volume (intensity) to its max, then back to its
minimum, giving us one *dum*. It then repeats
to give us another beat, and so on.
What the beats look like
● If we add we superimpose
the red wave to the blue
wave, we get a series of
beats (the purple wave)
● As we can see, it still keeps
its sinusoidal curves, but
the amplitudes are defined
by a boundary (the green
curves)
● The *dum*'s are distinct
because of that 0 amplitude
they sometimes get. That
pinches the sound making
you hear the beat clearly.
Mathematically Speaking
st=sm(cos(k1x−ω1t)+cos(k2x−ω2t))
s2=smcos(k2 x−ω2 t)
α=k1 x−ω1 t
β=k2 x−ω2t
Let:
Thus a superposition of s1 and s2 would be:
s1=smcos(k1 x−ω1t)
The two waves in math form
st=sm(cosα+cosβ)
Using Angle Addition and Half-angle Identities:
st=2∗sm(cos
(α+β)
2
)(cos
(α−β)
2
)
Substituting back alpha and beta:
st=2∗sm(cos
(k1x−ω1t+k2x−ω2t)
2
)(cos
(k1x−ω1t−k2x−ω2t)
2
)
Factoring:
st=2∗sm(cos(
(k1+k2)x
2
−
(ω1+ω2)t
2
))(cos(
(k1−k2)x
2
−
(ω1−ω2)t
2
))
We can thus note that beats have
Two frequencies governing them:
Mean angular frequency:
ω=
(ω1+ω2)
2
Angular frequency difference:
Δ ω=
(ω1−ω2)
2
What the beats look like
● These two frequencies
can be seen in the
graph:
● The mean angular
frequency is the
frequency of the purple
wave.
● The Angular frequency
difference is the
frequency of the green
curve enveloping the
beat.
References:
● Hawkes, Iqbal, Mansour, Milner-Bolotin, & Williams. (2015). Interference and Sound. In Physics for Scientists
and Engineers Revised Custom (Vol. 1, pp. 249-250). Toronto: Nelson Education.
● Made by: Arnold Leigh Ryan Choa 32038144

More Related Content

Recently uploaded

How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Celine George
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
mulvey2
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
RAHUL
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
GeorgeMilliken2
 
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
National Information Standards Organization (NISO)
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Nguyen Thanh Tu Collection
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
adhitya5119
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
Priyankaranawat4
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
Colégio Santa Teresinha
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
TechSoup
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Celine George
 
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdfবাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
eBook.com.bd (প্রয়োজনীয় বাংলা বই)
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
simonomuemu
 
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
sayalidalavi006
 
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Akanksha trivedi rama nursing college kanpur.
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 

Recently uploaded (20)

How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
 
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat  Leveraging AI for Diversity, Equity, and InclusionExecutive Directors Chat  Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
 
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdfবাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
 
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
 
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityNatural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 

Featured

2024 State of Marketing Report – by Hubspot
2024 State of Marketing Report – by Hubspot2024 State of Marketing Report – by Hubspot
2024 State of Marketing Report – by Hubspot
Marius Sescu
 
Everything You Need To Know About ChatGPT
Everything You Need To Know About ChatGPTEverything You Need To Know About ChatGPT
Everything You Need To Know About ChatGPT
Expeed Software
 
Product Design Trends in 2024 | Teenage Engineerings
Product Design Trends in 2024 | Teenage EngineeringsProduct Design Trends in 2024 | Teenage Engineerings
Product Design Trends in 2024 | Teenage Engineerings
Pixeldarts
 
How Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental HealthHow Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental Health
ThinkNow
 
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdfAI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
marketingartwork
 
Skeleton Culture Code
Skeleton Culture CodeSkeleton Culture Code
Skeleton Culture Code
Skeleton Technologies
 
PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024
Neil Kimberley
 
Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)
contently
 
How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024
Albert Qian
 
Social Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie InsightsSocial Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie Insights
Kurio // The Social Media Age(ncy)
 
Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024
Search Engine Journal
 
5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary
SpeakerHub
 
ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd
Clark Boyd
 
Getting into the tech field. what next
Getting into the tech field. what next Getting into the tech field. what next
Getting into the tech field. what next
Tessa Mero
 
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search IntentGoogle's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Lily Ray
 
How to have difficult conversations
How to have difficult conversations How to have difficult conversations
How to have difficult conversations
Rajiv Jayarajah, MAppComm, ACC
 
Introduction to Data Science
Introduction to Data ScienceIntroduction to Data Science
Introduction to Data Science
Christy Abraham Joy
 
Time Management & Productivity - Best Practices
Time Management & Productivity -  Best PracticesTime Management & Productivity -  Best Practices
Time Management & Productivity - Best Practices
Vit Horky
 
The six step guide to practical project management
The six step guide to practical project managementThe six step guide to practical project management
The six step guide to practical project management
MindGenius
 
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
RachelPearson36
 

Featured (20)

2024 State of Marketing Report – by Hubspot
2024 State of Marketing Report – by Hubspot2024 State of Marketing Report – by Hubspot
2024 State of Marketing Report – by Hubspot
 
Everything You Need To Know About ChatGPT
Everything You Need To Know About ChatGPTEverything You Need To Know About ChatGPT
Everything You Need To Know About ChatGPT
 
Product Design Trends in 2024 | Teenage Engineerings
Product Design Trends in 2024 | Teenage EngineeringsProduct Design Trends in 2024 | Teenage Engineerings
Product Design Trends in 2024 | Teenage Engineerings
 
How Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental HealthHow Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental Health
 
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdfAI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
 
Skeleton Culture Code
Skeleton Culture CodeSkeleton Culture Code
Skeleton Culture Code
 
PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024
 
Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)
 
How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024
 
Social Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie InsightsSocial Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie Insights
 
Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024
 
5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary
 
ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd
 
Getting into the tech field. what next
Getting into the tech field. what next Getting into the tech field. what next
Getting into the tech field. what next
 
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search IntentGoogle's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search Intent
 
How to have difficult conversations
How to have difficult conversations How to have difficult conversations
How to have difficult conversations
 
Introduction to Data Science
Introduction to Data ScienceIntroduction to Data Science
Introduction to Data Science
 
Time Management & Productivity - Best Practices
Time Management & Productivity -  Best PracticesTime Management & Productivity -  Best Practices
Time Management & Productivity - Best Practices
 
The six step guide to practical project management
The six step guide to practical project managementThe six step guide to practical project management
The six step guide to practical project management
 
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
 

CHOA lo2

  • 1. Beats From High to Low and Everything in Between
  • 2. What are beats? ● When you listen to a song, there are some portions where you can just hear a *dum dum dum* sound (*wub wub wub* in other cases), and, more often than not, we call those the beats of a song. ● 1 *dum*/*wub* = 1 beat ● But what are beats in the first place? And where do they come from?
  • 3. Learning Objectives ● Learn how beats are formed. ● Figure out what beats are: physically and mathematically. ● Visualize why there would be a distinct *dum* sound for beats
  • 4. How are beats formed? ● If you have tried plucking two strings of a guitar that are of different tones, you would have heard a faint *wub wub* sound. Congratulations! You have just made a beat! ● When two waves of close frequencies travel together I the same direction, at any given time, there will be places that are in-sync, constructively intefering with each other, places that are out of sync, destructively interfering with each other, and places in between.
  • 5. !!!NOTE!!! ● The two waves need to be travelling at the same direction and have the same amplitude in order to form a beat. ● They need to have the same amplitude to make a distinctive beat (one that pinches off to 0) ● They also need to be travelling in the same direction to be observable. Imagine Listening for two sounds one coming from the right (entering through the right ear), and one from the left (entering from the left ear): there wouldn't be physical interference happening.
  • 6. What are beats physically? ● If we slowed down that beat, we would hear a gradual increase from the beat's minimum volume (intensity) to its max, then back to its minimum, giving us one *dum*. It then repeats to give us another beat, and so on.
  • 7. What the beats look like ● If we add we superimpose the red wave to the blue wave, we get a series of beats (the purple wave) ● As we can see, it still keeps its sinusoidal curves, but the amplitudes are defined by a boundary (the green curves) ● The *dum*'s are distinct because of that 0 amplitude they sometimes get. That pinches the sound making you hear the beat clearly.
  • 8. Mathematically Speaking st=sm(cos(k1x−ω1t)+cos(k2x−ω2t)) s2=smcos(k2 x−ω2 t) α=k1 x−ω1 t β=k2 x−ω2t Let: Thus a superposition of s1 and s2 would be: s1=smcos(k1 x−ω1t) The two waves in math form st=sm(cosα+cosβ) Using Angle Addition and Half-angle Identities: st=2∗sm(cos (α+β) 2 )(cos (α−β) 2 ) Substituting back alpha and beta: st=2∗sm(cos (k1x−ω1t+k2x−ω2t) 2 )(cos (k1x−ω1t−k2x−ω2t) 2 ) Factoring: st=2∗sm(cos( (k1+k2)x 2 − (ω1+ω2)t 2 ))(cos( (k1−k2)x 2 − (ω1−ω2)t 2 )) We can thus note that beats have Two frequencies governing them: Mean angular frequency: ω= (ω1+ω2) 2 Angular frequency difference: Δ ω= (ω1−ω2) 2
  • 9. What the beats look like ● These two frequencies can be seen in the graph: ● The mean angular frequency is the frequency of the purple wave. ● The Angular frequency difference is the frequency of the green curve enveloping the beat.
  • 10. References: ● Hawkes, Iqbal, Mansour, Milner-Bolotin, & Williams. (2015). Interference and Sound. In Physics for Scientists and Engineers Revised Custom (Vol. 1, pp. 249-250). Toronto: Nelson Education. ● Made by: Arnold Leigh Ryan Choa 32038144