Free Pearson Edexcel International A Level Physics lesson

Investigate waves and electrical sources

Use practicals 4–8 to connect instrument readings with a physical model.

What you’ll learn

  • Analyse sound and string measurements with correct interval and mode counting.
  • Choose and evaluate optical measurement geometry.
  • Interpret resistance–length and terminal-voltage graphs without unsafe loading.

Core practicals 4 and 5: phase intervals and string modes

For sound speed, connect a generator and speaker and display a reference signal together with microphone output on a two-beam oscilloscope. Move the microphone along a measured path and identify repeated returns to the same relative phase. A distance spanning N full recurrences is N wavelengths, so divide by intervals rather than marked positions. Determine frequency from a calibrated source or the measured oscilloscope period, and use v = fλ.

For a vibrating string, a generator drives a controlled length while a stationary hanging mass over a suitable pulley provides approximately mg tension. Locate the fundamental or another explicitly identified mode. Change length, tension or mass per length one at a time and test f ∝ 1/L, f² ∝ T or f² ∝ 1/μ under fixed values of the other quantities. Weigh a long sample to obtain μ accurately enough for the intended comparison.

Both practicals require a stable pattern rather than merely a visually attractive signal. Reflections can distort microphone phase; a string can jump between modes or have uncertain effective node positions. Repeat the matching or resonance search, check results approached from different directions and record the relevant conditions. Keep sound moderate, secure vibrating equipment and use a catch tray under hanging masses. Greater drive amplitude can alter the model or increase risk without necessarily improving the result.

Sound: λ = Δx/N and v = fλ. String: f₁ = (1/2L)√(T/μ), with T ≈ mg only under the stated pulley/load conditions.

Symbols and units

  • Δx is microphone travel in m across N whole phase intervals
  • f is frequency in Hz
  • λ is wavelength in m
  • v is speed in m s⁻¹
  • string L is length in m, T is tension in N and μ is kg m⁻¹.

How the equation explains the idea

  1. For sound, divide the travel by the number of complete phase repeats to obtain λ, then multiply by source frequency to obtain v.
  2. For a fixed–fixed string, f₁ = √(T/μ)/(2L). At fixed tension and linear density, a graph of f₁ against 1/L is linear; at fixed L and μ, use f₁² against T. Do not confuse string tension T with wave period.

Worked example

Compare two interval counts

  1. Five successive same-phase microphone positions span 1.36 m.
  2. They contain four wavelength intervals, so λ = 1.36/4 = 0.340 m.
  3. At frequency 1000 Hz, sound speed is 340 m s⁻¹.

The phase-counting method and string-mode counting both depend on identifying intervals correctly.

Keep this idea. Count sound phase intervals and string half-wavelength loops explicitly, while controlling the conditions used in the model.

Core practical 6 and a refractive-index investigation

To determine a light wavelength, place a diffraction grating normal to a narrow beam and measure the geometry of identified diffraction maxima. Convert line density into slit spacing by taking its reciprocal with consistent units. If a screen is distance D from the grating and an order-m spot is transverse distance x from the central maximum, find θ = tan⁻¹(x/D), then λ = d sin θ/m. The central maximum itself has m = 0 and cannot supply λ through this equation.

Use maxima on both sides and repeat suitable measurements to check symmetry and alignment. Measure D from the grating plane, keep the screen appropriately oriented, and mark spot centres rather than uncertain edges. A larger separation can reduce fractional position uncertainty, but very high orders may be dim or geometrically inaccessible. Keep direct and diffracted beams below eye level, use a beam stop and avoid reflective objects. Never look into the grating to locate a beam.

For refractive index, trace a block, mark narrow incident and emergent rays, draw the normal and determine several incidence/refraction angles. Plot sin i against sin r to obtain the relative index from its slope. This practical shares geometric and angular uncertainties with the grating method but uses a different physical equation. Check alignment and a reasonable range of angles; more repeated readings cannot compensate for consistently measuring angles from the surface instead of the normal.

Grating: mλ = d sin θ, tan θ = x/D. Refraction: n₁ sin i = n₂ sin r.

Symbols and units

  • m is integer order, λ is wavelength in m and d is slit spacing in m
  • θ is diffraction angle
  • x and D are screen offset and distance in the same length unit
  • refractive indices are dimensionless.

How the equation explains the idea

  1. Find θ from tan θ = x/D, then calculate λ = d sin θ/m. For a large angle, replacing sin θ by x/D is not justified.
  2. For an index investigation, Snell’s law gives sin i = (n₂/n₁)sin r. Plotting sin i vertically against sin r horizontally gives the index ratio; the reverse axes give its reciprocal.

Worked example

Use the full screen geometry

  1. A first-order spot is 0.30 m from the centre on a screen 1.00 m away; spacing d = 2.0 μm.
  2. sin θ = x/√(x² + D²) = 0.30/√1.09 ≈ 0.2873.
  3. λ = 2.0 × 10⁻⁶ × 0.2873 = 5.75 × 10⁻⁷ m.

At this angle, x/D is a tangent; using it as the sine introduces a systematic approximation error.

Keep this idea. Use the correct optical geometry, order, line spacing and angle reference before evaluating the data.

Core practicals 7 and 8: geometry or source behaviour?

In a resistivity investigation, measure the potential difference across several lengths of a uniform wire and the current through each selected length. Keep material, area and temperature approximately fixed, determine resistance V/I and plot R against L. Measure corrected diameter at several positions and orientations to obtain area. Multiplying the fitted resistance–length gradient by area gives resistivity; a constant contact or lead contribution can appear as an intercept.

In a cell investigation, vary a safe external load and record terminal voltage and circuit current together. Plot V against I, whose slope is −r and vertical intercept is ε under the constant-parameter source model. Place the voltmeter across the cell and ammeter in series, use appropriate meter ranges and include a switch and current limit. Do not try to measure the current-axis intercept by directly short-circuiting the cell.

Both experiments can be distorted by heating, unstable contacts and meter loading, but their conclusions differ. A high-resistance voltmeter usually reduces unwanted current draw. Brief low-current measurements and cooling intervals can help stabilise the wire or cell. Repeat a reference setting later in the sequence to check drift rather than assuming that a smooth graph proves unchanging conditions. State which slope, geometry measurement and uncertainty source are relevant to the requested result, and preserve the original voltage/current pairs for checking.

Wire: R = (ρ/A)L + Rextra. Cell: V = ε − rI. Pheating = I²R for an appropriate resistance.

Symbols and units

  • R is resistance in Ω, L is wire length in m, ρ is resistivity in Ω m and A is area in m²
  • V and ε are terminal voltage and emf in V
  • I is current in A and r is internal resistance in Ω.

How the equation explains the idea

  1. For a wire, R = (ρ/A)L + Rextra gives positive gradient ρ/A and a possible contact-resistance intercept. For a supplying cell, V = ε − rI gives negative gradient −r and emf intercept.
  2. Identify the plotted quantities before interpreting a slope. Reduce current or measurement duration to limit heating; changing resistance during the run invalidates a constant-resistance fit.

Worked example

Do not mix the two slopes

  1. A wire R-versus-L slope is 8.0 Ω m⁻¹ with area 5.0 × 10⁻⁸ m², giving ρ = 4.0 × 10⁻⁷ Ω m.
  2. A cell V-versus-I slope is −0.80 V A⁻¹, giving r = 0.80 Ω.
  3. Only the wire calculation requires the cross-sectional area factor.

The axis units expose why the two gradients represent different quantities.

Keep this idea. Choose the circuit connections and graph from the intended property, then check heating, contacts and loading.

Open the interactive lesson for free practice and reviewed three-question samples when available. New full question sets and timed unit checks are in preparation. Existing complete Physics revision packs retain paid access; existing free teaching PDFs remain free.

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