RP: Investigating Stationary Waves

• What is the overall aim of the experiment?

  Measure frequency of the first harmonic

  
• What are the independent and dependent variables in the experiment?

  • Independent variable: length, tension, or mass per unit length
  • Dependent variable: frequency of the first harmonic

  
• What are the control variables when varying length?

  • Same masses attached (tension)
  • Same string (mass per unit length)
• What are the control variables when varying tension?

  • Same length of the string
  • Same string (mass per unit length)
• What are the control variables when varying mass per unit length?

  • Same masses attached (tension)
  • Same length of the string
• What is the resolution of a metre ruler?

  1 mm
• What is the resolution of a top-pan balance?

  0.005 g
• What is the method for measuring the frequency of the first harmonic?

  1. Set up apparatus with string and vibration generator
  2. Measure length L from generator to bridge
  3. Turn on signal generator
  4. Increase frequency until first harmonic is observed
  5. Repeat with different lengths
  6. Take average of frequency readings
  7. Measure tension using $T =$$mg$

  
• What is the formula for tension in the string?

  $T =$$mg$
• What is the formula for mass per unit length?

  $\mu =$$\text{mass of string} \div \text{length of string}$
• What is the relationship for the first harmonic wavelength?

  • Wavelength, $\lambda =$$2L$
• What is the speed of the stationary wave formula?

  • Speed, $v =$$f\lambda =$$f \times 2L$
• How can frequency be rearranged from the wave speed equation?

  $f =$$v/(2L)$
• What is the graphing relationship for frequency and length?

  • Plot mean values of $f$ against $1/L$
  • Gradient = $v/2$

  
• What is the gravitational field strength on Earth?

  $9.81 \text{ N kg}^{-1}$
• What are the types of errors in the experiment?

  • Systematic errors
  • Random errors
• How can systematic errors be minimized?

  • Use an oscilloscope for verification
  • Stabilize the signal generator for 20 minutes
• What is the best practice for measuring frequency accurately?

  • Adjust frequency while observing a node
  • Note frequency at largest vibration
• What safety considerations should be taken?

  • Use rubber string or wear goggles
  • Stand away from falling masses
  • Use crash mat under masses
• What should be done before conducting an experiment?

  • Set up a table for measurements
• How can uncertainties in measurements be assessed?

  • Calculate uncertainty in wave speed
• How is wave speed verified in the experiment?

  • Using the equation for tension and mass per unit length

  
• What is the significance of measuring multiple half-wavelengths?

  • Increases measurement resolution
• What is the technique to resolve random errors in frequency measurement?

  • Adjust frequency while observing a node
• What is the procedure for taking repeat measurements of frequency?

  1. Note frequency at largest vibration
  2. Increase frequency, then reduce to observe first harmonic
  3. Average three readings
• What is the importance of using a rubber string?

  • Prevents injury if it snaps under tension
• Why should goggles be worn when using metal wire?

  • Protects eyes in case of snapping
• What should be done to ensure safety with falling masses?

  • Stand away and use a crash mat