Lab
Relationship Between Tension in a String and Wave Speed
Printer Friendly Version
We have observed that an increase in the tension of a string causes an increase in the velocity that waves travel on the string. In this activity we will examine the precise relationship between tension (T) the force applied to the string, the wave speed (v
_{w}
) and the linear mass density of the string (µ = m/L which is measured in kg/m).
We will stretch a string across two “bridges”, creating two fixed ends, and then allow the remaining string to hang over a supporting bar with different increments of mass generating its tension. This will allow us to increase tension in the string by the addition of mass, while keeping a constant wavelength. This will cause the velocity to change with the frequency of the string like a guitar with its tuning pegs.
A microphone will be placed next to the string and when plucked the frequency of the note will be displayed on a scale using a frequency analyzer. Notice that several frequencies are observed, the must discernible and lowest frequency represents the fundamental - seen as a dark red line with green/yellow highlights. The other frequencies represent higher harmonics (or overtones). You can notice that they are evenly spaced in frequency as predicted by our model of standing waves.
Measuring the length of the vibrating string allows us to calculate the wavelength. Then by focusing on the fundamental frequency (which has only one loop) and using our model for fixed-fixed standing waves we can determine the wave speed along the string.
Refer to the following information for the next question.
Part A: Data Collection
The experiment will be performed on two fishing lines having different pound-tests or linear density.
Record below the length of the
first vibrating string segment - the heavy string
.
L
_{1}
= ______________ m
Complete the following table by measuring calculating the required values for string one.
Record below the length of the
second vibrating string segment - the light string
.
L
_{2}
= ______________ m
Complete the following table by measuring calculating the required values for string two.
Samples of each of these fishing lines will now be provided to you so that you can measure their mass and length. This information will allow you to determine the
linear mass density
for each type of string used in the experiment.
Refer to the following information for the next three questions.
String #1 (Heavy String)
length of sample in meters
mass of sample in kilograms
linear mass density (µ = m/l) in kg/m
Refer to the following information for the next three questions.
String #2 (Light String)
length of sample in meters
mass of sample in kilograms
linear mass density (µ = m/l) in kg/m
Refer to the following information for the next five questions.
Part B: EXCEL
Using EXCEL, graph
Wave Speed vs Tension
for both data sets and then
Wave Speed Squared vs Tension
for both data sets.
What is the filename of your group's EXCEL workbook?
On the graph of
Wave Speed vs Tension
, what is the
exponent
on
x
for your group's heavy string?
On the graph of
Wave Speed vs Tension
, what is the
exponent
on
x
for your group's light string?
When rectified, what is the
slope
of your group's graph for
Wave Speed Squared vs Tension
for your group's heavy string?
When rectified, what is the
slope
of your graph for
Wave Speed Squared vs Tension
for your group's light string?
Refer to the following information for the next seven questions.
Part C: Conclusions
The equation relating wave speed and tension in a string is given as
To make this equation fit our lines, we must square both sides
This solution tells us that the slopes of your lines for
Wave Speed Squared vs Tension
represent the reciprocal of each string's linear mass density, µ.
What is the reciprocal of your heavy line's slope? (give your answer to three significant digits)
Based on your measured values calculated using the sample's mass and length, in Part B above, what was your group's percent difference for the heavy string's linear mass density?
What is the reciprocal of your light line's slope? (give your answer to three significant digits)
Based on your measured values calculated using the sample's mass and length, in Part B above, what was your group's percent difference for the light string's linear mass density?
Waves are created on two ropes, a thick rope and a thin rope. If the tension on each of the ropes is the same, what is true about the wave speeds?
a. The thick rope has a higher waves speed.
b. The thin rope has a higher wave speed.
c. The two ropes have the same wave speed because they are under the same tension.
2. What would be true about the frequency for the two ropes in question #1, if the wavelength was kept constant?
a. The thicker rope will have a greater frequency
b. The thinner rope will have a greater frequency
c. The two ropes will have the same frequencies
Which of the following statements are true about waves traveling on strings?
a. Wave Speed is Proportional to the Tension on the String
b. Wave Speed is Proportional to the Square of Tension on the String
c. The Square of the Wave Speed is Inversely Proportional to the Linear Density of the String
d. The Square of the Wave Speed is Proportional to the Linear Density of the String
e. The Square of the Wave Speed is Proportional to the Tension on the String
f. The Wave Speed is Inversely Proportional to the Tension on the String
Related Documents
Lab:
Labs -
Coefficient of Friction
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Directions: Constructive and Destructive Interference
Labs -
Doppler Effect: Source Moving
Labs -
Falling Coffee Filters
Labs -
Frequency of Vibrating Strings
Labs -
Illuminance by a Light Source
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
Interference Shading
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Pipe Music
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Sample Solutions
Labs -
Ripple Tank Student Involvement Sheet
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Speed of a Wave Along a Spring
Labs -
Speed of Sound in Air
Labs -
Speed of Sound in Copper
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video: Law of Reflection
Labs -
Video: Law of Reflection Sample Diagram
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Barrier Waves, Bow Waves, and Shock Waves
RL -
Beats: An Example of Interference
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Interference of Waves
RL -
Interference: In-phase Sound Sources
RL -
Introduction to Sound
RL -
Law of Reflection
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Physical Optics - Thin Film Interference
RL -
Properties of Friction
RL -
Resonance in Pipes
RL -
Resonance in Strings
RL -
Ripple Tank Video Guides
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Sound Level Intensity
RL -
Speed of Waves Along a String
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Doppler Effect
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
Vibrating Systems - Simple Pendulums
RL -
Vibration Graphs
RL -
Wave Fundamentals
RL -
Waveform vs Vibration Graphs
RL -
Welcome! What is Mass?
RL -
Work and Energy
REV -
Orbitals
Review:
REV -
Chapter 26: Sound
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Sound
REV -
Waves and Sound
REV -
Waves and Sound
Worksheet:
APP -
Big Fist
APP -
Echo Chamber
APP -
Family Reunion
APP -
The Antelope
APP -
The Box Seat
APP -
The Dog-Eared Page
APP -
The Jogger
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Light Properties
CP -
Mobiles: Rotational Equilibrium
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Reflection
CP -
Shock Waves
CP -
Sound
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
CP -
Waves and Vibrations
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Apparent Depth
NT -
Atmospheric Refraction
NT -
Concert
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Light vs Sound Waves
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Scale Reading
NT -
Settling
NT -
Shock Cone
NT -
Skidding Distances
NT -
Sound Waves
NT -
Spiral Tube
NT -
Standing Waves
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Beats
WS -
Beats, Doppler, Resonance Pipes, and Sound Intensity
WS -
Combining Kinematics and Dynamics
WS -
Counting Vibrations and Calculating Frequency/Period
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Doppler - A Challenge Problem
WS -
Doppler Effect
WS -
Fixed and Free-end Reflections
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Fundamental Wave Terms
WS -
Illuminance 1
WS -
Illuminance 2
WS -
Interference: In-phase Sound Sources
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
More Practice with Resonance in Pipes
WS -
More Practice with the Doppler Practice
WS -
net F = ma
WS -
Practice with Resonance in Pipes
WS -
Practice with the Doppler Effect
WS -
Practice: Speed of a Wave Along a String
WS -
Practice: Vertical Circular Motion
WS -
Pulse Superposition: Interference
WS -
Ripple Tank Review
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Sound Vocabulary
WS -
Speed of Sound
WS -
Speed of Sound (Honors)
WS -
Standard Model: Particles and Forces
WS -
Standing Wave Patterns #1
WS -
Standing Wave Patterns #2
WS -
Standing Wave Patterns #3
WS -
Standing Wave Patterns #4
WS -
Static Springs: The Basics
WS -
Vibrating Systems - Period and Frequency
WS -
Vocabulary for Newton's Laws
WS -
Wave Phenomena Reading Guide
WS -
Wave Pulses
WS -
Waveform and Vibration Graphs #1
WS -
Waveform and Vibration Graphs #2
WS -
Work and Energy Practice: Forces at Angles
TB -
25A: Introduction to Waves and Vibrations
TB -
25B: Vibrations and Waves
TB -
25C: Wave Speed
TB -
25D: Interference
TB -
25E: Doppler
TB -
25F: Doppler Effect (continued)
TB -
26B: Speed of Sound
TB -
26C: Resonance
TB -
26D: Beats
TB -
26E: Decibels
TB -
27A: Light Properties
TB -
Decibels and Sound Intensity #1
TB -
Decibels and Sound Intensity #2
TB -
Interference Re-examined
TB -
Refraction Phenomena Reading Questions
TB -
Sound: Mixed Practice
TB -
Systems of Bodies (including pulleys)
TB -
Waves and Vibrations
TB -
Work, Power, Kinetic Energy
Copyright © 2007-2015
William A. Hilburn
All rights reserved.