Seneca
Sign up

Stationary Waves 2

Physics: AQA A Level, topic 3.1.7

Stationary 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.

Set up equipment as shown

Set up equipment as shown

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.

Stationary 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.

Test yourself on Stationary Waves 2

  • What does the pattern of the first harmonic of a stationary wave look like?

  • How do you find the mass per unit length of the string?

  • In the stationary wave of a string practical, what is the relationship between length of string and frequency and why?

  • In the stationary wave of a string practical, what is the relationship between mass per unit length of string and frequency and why?

  • In the stationary wave of a string practical, what is the relationship between tension in the string and frequency and why?

Practise this topic for free