3.5.2

Standing Waves 2

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Standing Wave Practical

This practical investigates how the frequency of stationary waves on a string changes when length, tension and mass per unit length are changed.

Initial measurements

Initial measurements

  • Measure the length of the string, the tension in the string and the mass per unit length.
  • The tension can be calculated by multiplying the total mass of the masses and the acceleration due to gravity.
    • T=mgT = mg
  • The mass per unit length can be calculated by dividing the total mass of the string by its length.
    • μ=Ml\mu = \frac{M}{l}
Determine frequency of first harmonic

Determine frequency of first harmonic

  • This can be found by varying the frequency until you see the pattern needed for the first harmonic.
    • Two nodes at each end of the string with one antinode in the centre.
Change variable - length

Change variable - length

  • To investigate how changing the length affects the resonant frequency, keep the tension and mass per unit length the same.
  • Vary the length of the string by moving the oscillator away or toward the pulley.
  • At each string length, find the new first harmonic.
  • Plot a graph of f against l.
Change variable - mass per unit length

Change variable - mass per unit length

  • To investigate how changing μ affects the resonant frequency, keep the tension and length the same.
  • Vary μ by using different types of material for the string.
  • For each material (with a different value of μ), find the new first harmonic.
  • Plot a graph of μ against f.
Change variable - tension

Change variable - tension

  • To investigate how changing tension affects the resonant frequency, keep the length and mass per unit length the same.
  • Vary the tension in the string by varying the mass attached to the end.
  • At each value of tension, find the new first harmonic.
  • Plot a graph of f against T.

Standing Wave Practical - Results

The frequency of the first harmonic of a string can be calculated using an equation. The practical shown previously should show certain relationships.

First harmonic equation

First harmonic equation

  • We expect that the frequency of the first harmonic should be given by:
    • f=12lTμf = \frac{1}{2l}\sqrt{\frac{T}{\mu}}
Relationship with length

Relationship with length

  • The longer the length of the string, the lower the frequency.
  • This is because the longer the length is, the longer the half wavelength must be, and so the lower the frequency.
Relationship with μ

Relationship with μ

  • The larger the mass per unit length, μ, the lower the resonant frequency.
  • For the same length string, waves travel more slowly through a heavier string, so the frequency must be lower.
    • Remember f=vλf = \frac{v}{\lambda}
Relationship with tension

Relationship with tension

  • The higher the tension in the string, the higher the frequency.
  • This is because waves travel more quickly down a string with higher tension.
Jump to other topics
1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics1.1.2Graphs of Motion1.1.3Uniform Acceleration Equations1.1.4Projectile Motion1.1.5Bouncing Ball Example
1.2

Forces

1.2.1Friction1.2.2Terminal Speed1.2.3Newton's Laws1.2.4Exam-Style Question - Forces1.2.5End of Topic Test - Newton's Third Law
1.3

Momentum & Impulse

1.3.1Momentum1.3.2Momentum 21.3.3End of Topic Test - Newton's Laws & Momentum
1.4

Work, Energy & Power

1.4.1Work & Energy1.4.2Conservation of Energy1.4.3Power & Efficiency1.4.4IB Multiple Choice- Work, Energy & Power
2

The Particulate Nature of Matter

2.1

Thermal Concepts

2.1.1Molecular Kinetic Theory Model2.1.2Molecular Kinetic Theory Model 22.1.3Thermal Energy Transfer2.1.4Thermal Energy Transfer Experiments2.1.5Thermal Equilibrium2.1.6Thermal Conductivity2.1.7Heat Energy Transfer
2.2

Modelling a Gas

2.2.1Ideal Gases2.2.2Ideal Gases 22.2.3End of Topic Test - Thermal Energy & Ideal Gases2.2.4Exam-Style Question - Ideal Gases
3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves3.1.2Simple Harmonic Motion
3.2

Travelling Waves

3.2.1Wave Speed & Phase Difference3.2.2Longitudinal & Transverse Waves3.2.3Electromagnetic Waves3.2.4Electromagnetic Waves 23.2.5Sound Waves
3.3

Wave Characteristics

3.3.1Polarisation
3.4

Wave Behaviour

3.4.1Reflection & Absorption3.4.2Reflection of Light3.4.3Refraction3.4.4Refractive index
3.5

Standing Waves

3.5.1Standing Waves3.5.2Standing Waves 23.5.3End of Topic Test - Standing Waves3.5.4IB Multiple Choice - Waves
3.6

Simple Harmonic Motion

3.6.1Simple Harmonic Motion3.6.2Simple Harmonic Systems3.6.3Energy in Simple Harmonic Motion3.6.4End of Topic Test - Simple Harmonic Motion3.6.5End of Topic Test - Simple Harmonic Motion
3.7

Single Slit Diffraction

3.7.1Diffraction
3.8

Interference

3.8.1Interference3.8.2Interference 23.8.3Diffraction Gratings3.8.4End of Topic Test - Diffraction
3.9

Doppler Effect

3.9.1Doppler Effect
4

Fields

4.1

Circular Motion

4.1.1Circular Motion4.1.2Centripetal Force4.1.3IB Multiple Choice - Circular Motion
4.2

Newton's Law of Gravitation

4.2.1Newton's Law4.2.2Orbits of Planets & Satellites4.2.3Escape Velocity & Synchronous Orbits4.2.4End of Topic Test - Gravitational Fields
4.3

Fields

4.3.1Fields4.3.2Gravitational Field Strength4.3.3Gravitational Potential4.3.4Electric Field Strength4.3.5Electrostatic & Gravitational Forces4.3.6Electric Potential4.3.7IB Multiple Choice - Gravitational Fields
4.4

Fields at Work

4.4.1Radial Field Strength4.4.2Orbits of Planets & Satellites4.4.3Escape Velocity & Synchronous Orbits4.4.4End of Topic Test - Gravitational Fields4.4.5Uniform Electric Fields4.4.6IB Multiple Choice - Electric Field & Potential
4.5

Electric Fields

4.5.1Electric Charge4.5.2Conservation of Charge4.5.3Coulomb's Law4.5.4Current4.5.5Potential Difference4.5.6IB Multiple Choice - Electric Charge
4.6

Magnetic Effect of Electric Currents

4.6.1Magnetism4.6.2Magnetic Field4.6.3Magnetic Force4.6.4Moving Charges in a Magnetic Field4.6.5IB Multiple Choice - Magnetism
4.7

Heating Effect of Currents

4.7.1Circuits4.7.2Resistance4.7.3Power and Conservation4.7.4IB Multiple Choice - DC Circuits
4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction4.8.2Electromagnetic Induction 24.8.3Magnetic Flux & Flux Linkage4.8.4End of Topic Test - Electromagnetic Induction
4.9

Power Generation & Transmission

4.9.1Alternating Currents4.9.2Operation of a Transformer
4.10

Capacitance

4.10.1Capacitance4.10.2Parallel Plate Capacitor4.10.3Energy Stored by a Capacitor4.10.4Capacitor Discharge4.10.5Capacitor Charge4.10.6Magnetic Flux Density4.10.7End of Topic Test - Capacitance & Flux Density
5

Nuclear & Quantum Physics

5.1

Discrete Energy & Radioactivity

5.1.1Atomic Spectra5.1.2Atomic Structure5.1.3Photons5.1.4Discrete Energy Levels5.1.5Alpha, Beta & Gamma Radiation5.1.6Scientific Practices - Unstable Nuclei5.1.7Radioactive Decay5.1.8IB Multiple Choice - Atomic Physics
5.2

Nuclear Reactions

5.2.1Mass & Energy5.2.2Nuclear Fission
5.3

The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons5.3.2Particle Interactions5.3.3Classification of Particles5.3.4Wave-Particle Duality5.3.5Wave Functions & Probability5.3.6IB Multiple Choice - Quantum Physics
5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay5.4.2Nuclear Radius5.4.3IB Multiple Choice - Nuclear Physics
6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units6.1.2SI Prefixes, Standard Form & Converting Units6.1.3End of Topic Test - Units & Prefixes
6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements6.2.2Uncertainty6.2.3Estimation6.2.4End of Topic Test - Measurements & Errors
6.3

Vectors & Scalars

6.3.1Scalars & Vectors6.3.2Vector Problems

Practice questions on Standing Waves 2

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What does the pattern of the first harmonic of a standing wave look like?Multiple choice
  2. 2
    How do you find the mass per unit length of the string?Multiple choice
  3. 3
    In the stationary wave of a string practical, what is the relationship between length of string and frequency and why?Flashcard
  4. 4
    In the stationary wave of a string practical, what is the relationship between mass per unit length of string and frequency and why?Flashcard
  5. 5
    In the stationary wave of a string practical, what is the relationship between tension in the string and frequency and why?Flashcard
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Standing Waves

End of Topic Test - Standing Waves