Lab
Frequency of Vibrating Strings
Printer Friendly Version
Wave speed is dependent upon the medium through which the wave is traveling. By changing a medium you can change the wave speed. Usually any change in velocity will be balanced by an equivalent change in the wavelength - this phenomena is called refraction.
Our "string medium" can be altered by changing the tension under which it is placed. Since our apparatus regulates each string's fundamental wavelength, the greater the tension, the faster the wave travels, and therefore the higher the frequency of that string.
The new speed of the wave depends on not only the tension but the mass per unit length of the string; a quantity referred to as its linear mass density. The mathematical relationship of wave speed, tension, and linear mass density is:
In this lab you will be tuning five strings (of different linear density) to the same pitch(frequency). Since the strings have the same fundamental wavelength, this means that waves traveling along each string must have the same wave speed. By measuring the tension and linear density of each string we will be able to determine the velocity of the waves along each string. Then by measuring fundamental wavelength we can determine the frequency at which the string is vibrating.
Before you begin, open the spreadsheet entitled 1-WaveTensionLab.xls in your period folder and resave it as
LastnameLastname-WavetensionLab.xls
so that you can immediately begin recording and saving your data.
What is the name of your file?
What is the number of your apparatus?
Refer to the following information for the next question.
Recording values to determine the mass/length of each string
Our first step is to determine the mass per unit length of each vibrating string. To do this, you will mass and measure the length of five equivalent "sample strings." Record your results here and in your EXCEL spreadsheet.
On the data tab, what is the slope of the line of best fit for your graph of
Mass/Length vs Pound Rating
?
Refer to the following information for the next two questions.
Procedure to obtain values of common frequencies
An apparatus should be setup at your station that resembles the above diagram.
Hang two 200-gram masses off of the 1st string (the 30-lb test, or the “heaviest string). Each lab group should have several masses with paper clips connected to them to help suspend the masses from the end of each string.
Starting with a 200-gram mass on the 2nd string 20-lb test), continue to add mass (washers) until the two frequencies (notes) are the same.
Hint:
To help hear the sound better bite on one end of a wooden stick while the other end is touching the apparatus.
Starting with a 100-gram mass on the 3rd string (15-lb test), continue to add mass (washers) until all three play the same note (have the same frequency).
Starting with a 50-gram mass on the 4th string (8-lb test), continue to add mass (washers) until all five strings have the same frequency.
Once your group feels that all five strings have the "same" frequency, measure the distance between the fixed ends of each string. Then carefully remove the hanging masses from each string and measure their total mass in grams. Record your values in the table below and also in your EXCEL spreadsheet.
Average the lengths of the five vibrating strings and record its value in your EXCEL spreadsheet. Since the length of a loop equals ½
l
, you can now calculate the wavelength of the waves traveling through each string.
What is the average length (in cm) of your vibrating fishing lines?
What was the average wavelength (in meters) of the waves traveling through the fishing lines on your apparatus?
Refer to the following information for the next seven questions.
Analysis and Conclusions
On the graph tab, what is the slope of your line of best fit for the graph
String Tension vs Linear Mass Density
?
What is this line's y-axis intercept?
What was the speed of the waves (in m/sec) traveling through the fishing lines on your apparatus?
Based on your slope, what was the common frequency (in hertz) of your five strings?
Based only on the data for the 50-lb test string, what was the desired frequency (in hertz) that you were trying to match in the other four strings?
What is the percent error between the frequency based on the 50-lb test string and the common frequency based on your line's slope?
An octave represents a doubling of the frequency, how much mass would need to be added to increase the frequency of the 50-lb test string by an octave?
Related Documents
Lab:
Labs -
Directions: Constructive and Destructive Interference
Labs -
Doppler Effect: Source Moving
Labs -
Illuminance by a Light Source
Labs -
Inertial Mass
Labs -
Interference Shading
Labs -
Pipe Music
Labs -
Relationship Between Tension in a String and Wave Speed
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 -
Video: Law of Reflection
Labs -
Video: Law of Reflection Sample Diagram
Resource Lesson:
RL -
Barrier Waves, Bow Waves, and Shock Waves
RL -
Beats: An Example of Interference
RL -
Interference of Waves
RL -
Interference: In-phase Sound Sources
RL -
Introduction to Sound
RL -
Law of Reflection
RL -
Physical Optics - Thin Film Interference
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 -
The Doppler Effect
RL -
Vibrating Systems - Simple Pendulums
RL -
Vibration Graphs
RL -
Wave Fundamentals
RL -
Waveform vs Vibration Graphs
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 -
Echo Chamber
APP -
The Dog-Eared Page
CP -
Light Properties
CP -
Reflection
CP -
Shock Waves
CP -
Sound
CP -
Waves and Vibrations
NT -
Apparent Depth
NT -
Atmospheric Refraction
NT -
Concert
NT -
Light vs Sound Waves
NT -
Shock Cone
NT -
Sound Waves
NT -
Standing Waves
WS -
Beats
WS -
Beats, Doppler, Resonance Pipes, and Sound Intensity
WS -
Counting Vibrations and Calculating Frequency/Period
WS -
Doppler - A Challenge Problem
WS -
Doppler Effect
WS -
Fixed and Free-end Reflections
WS -
Fundamental Wave Terms
WS -
Illuminance 1
WS -
Illuminance 2
WS -
Interference: In-phase Sound Sources
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
More Practice with Resonance in Pipes
WS -
More Practice with the Doppler Practice
WS -
Practice with Resonance in Pipes
WS -
Practice with the Doppler Effect
WS -
Practice: Speed of a Wave Along a String
WS -
Pulse Superposition: Interference
WS -
Ripple Tank Review
WS -
Sound Vocabulary
WS -
Speed of Sound
WS -
Speed of Sound (Honors)
WS -
Standing Wave Patterns #1
WS -
Standing Wave Patterns #2
WS -
Standing Wave Patterns #3
WS -
Standing Wave Patterns #4
WS -
Vibrating Systems - Period and Frequency
WS -
Wave Phenomena Reading Guide
WS -
Wave Pulses
WS -
Waveform and Vibration Graphs #1
WS -
Waveform and Vibration Graphs #2
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 -
Waves and Vibrations
Copyright © 2007-2017
William A. Hilburn
All rights reserved.