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The Electric Guitar

Key idea: Explain how a guitar pickup uses changing magnetic flux to induce an a.c. signal in a coil that matches the string’s vibration frequency (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Use magnetic flux and flux-linkage relationships.
  • Apply Faraday's and Lenz's laws to induced e.m.f. and direction.
  • Explain simple applications of electromagnetic induction, including motional e.m.f. and eddy currents.
  • Explain simple iron-core transformer operation and apply ideal transformer ratios.

1. Definitions (Must Know)

A. Pickup coil (idea)

An electric guitar pickup uses a magnet and a coil so that string vibration changes magnetic flux linkage and induces an a.c. e.m.f.

2. Key Ideas (What Earns Marks)

  • A magnetised string moving near a coil changes the flux linkage NΦ.
  • Changing flux linkage induces an e.m.f.: ε = -d(NΦ)/dt
  • Faster / larger vibration usually increases |d(NΦ)/dt| and increases signal amplitude.
Scope note

This is a qualitative induction application (18f). You do not need amplifier electronics.

3. Detailed Explanations

A. Step-by-step chain

  1. A permanent magnet magnetises the nearby metal string.
  2. When the string vibrates, the magnetic field near the coil changes.
  3. Flux linkage through the coil changes with time.
  4. An a.c. e.m.f. is induced in the coil, which is amplified and sent to a speaker.

4. Common Mistakes

  • Saying “the coil makes the string vibrate” (it mainly detects vibration).
  • Forgetting that the output is typically an a.c. signal (because the flux changes back and forth).

5. Exam Tips

  • Use the phrase “changing flux linkage induces an a.c. e.m.f.”.
  • If asked about frequency: “the induced signal has the same frequency as the string vibration”.

6. Worked Examples

Modelled example 1

Frequency link

Core

Problem

A string vibrates at 440 Hz. What is the frequency of the induced e.m.f. in the pickup, in an idealised model?
Study the worked solution

  1. Relate motion to flux

    Method

    The string makes the pickup’s flux linkage vary once per vibration cycle.

    Reason

    The idealised string position pattern repeats every vibration period.

    Working

    f_NΦ = f_string

  2. Relate flux to e.m.f.

    Method

    The induced e.m.f. repeats at the same fundamental frequency.

    Reason

    Differentiating a periodic sinusoidal linkage changes phase and amplitude, not its frequency.

    Working

    E = -d(NΦ)/dt

  3. State the result

    Method

    f_E = 440 Hz.

    Reason

    The pickup output follows the string’s fundamental vibration rate in this idealisation.

    Working

    f_E = f_string = 440 Hz

Guided practice 2

Why is the signal a.c.?

About 4 min

Problem

Explain why the pickup output is typically an a.c. signal rather than a steady d.c. voltage.

Try this before viewing the solution

Cause of alternating polarity

Hints

Hint 1: track one full vibration
During one half-cycle flux linkage changes one way; during the other it changes the opposite way.
Hint 2: retain the sign
Use the minus sign in E = -d(NΦ)/dt to infer what happens to output polarity.
View solution step by step

  1. Follow the linkage

    Method

    String vibration makes flux linkage increase and decrease repeatedly.

    Reason

    The magnetised string moves back and forth relative to the pickup.

    Working

    NΦ(t) oscillates

  2. Follow the derivative

    Method

    d(NΦ)/dt repeatedly changes sign.

    Reason

    The linkage alternates between increasing and decreasing.

    Working

    d(NΦ)/dt: +,-, +,-,…

  3. Infer the output

    Method

    The induced e.m.f. reverses polarity, so the output is a.c.

    Reason

    Faraday’s law gives an e.m.f. sign opposite to the instantaneous linkage-change sign.

    Working

    E = -d(NΦ)/dt

Common misconception 3

Non-magnetic string

Find and correct the mistake

Learner claim

A non-magnetic nylon string vibrates with the same motion as a metal string. A learner says the pickup signal is unchanged because the vibration is unchanged. Diagnose the claim.

Try this before viewing the solution

Expected signal

View solution step by step

  1. Identify the missing link

    Method

    The pickup magnet does not magnetise nylon appreciably.

    Reason

    Nylon is non-magnetic in this application.

    Working

    nylon ⇒ negligible magnetisation

  2. Compare linkage changes

    Method

    The same mechanical vibration causes a much smaller change in the coil’s flux linkage.

    Reason

    The moving string no longer perturbs the magnetic field strongly.

    Working

    |Δ(NΦ)|↓

  3. Correct the signal claim

    Method

    The induced pickup signal becomes very small.

    Reason

    Smaller flux-linkage change per time gives smaller induced e.m.f.

    Working

    |d(NΦ)/dt|↓ ⇒ |E|↓

Examiner practice 4

Doubling the number of turns

3 marks

Examination question

The pickup coil’s number of turns is doubled while the flux change per turn stays the same. State and explain the effect on induced e.m.f. amplitude. [3 marks]

Try this before viewing the solution

View solution step by step

  1. Name the relevant quantity

    1 mark

    Method

    Faraday’s law uses total flux linkage NΦ.

    Reason

    Each linked turn contributes to the induced e.m.f.

    Working

    E = -d(NΦ)/dt

  2. Apply the change

    1 mark

    Method

    Doubling N doubles the rate of total linkage change.

    Reason

    The flux history per turn is stated to remain the same.

    Working

    N → 2N ⇒ d(NΦ)/dt → 2d(NΦ)/dt

  3. State the signal effect

    1 mark

    Method

    The induced e.m.f. amplitude approximately doubles.

    Reason

    Its amplitude is proportional to the linkage-change-rate amplitude.

    Working

    E₀ → 2E₀

Challenge 5

Larger vibration amplitude

Minimal support

Independent transfer

The string vibrates at the same frequency but with larger displacement amplitude. What happens to the pickup output amplitude, qualitatively?

Try this before viewing the solution

Pickup output amplitude

Hints

Hint 1: separate amplitude from frequency
The period stays the same; compare how much the flux linkage changes during that period.
View solution step by step

  1. Hold frequency fixed

    Method

    The cycle time is unchanged.

    Reason

    The vibration frequency is explicitly held constant.

    Working

    f = constant ⇒ T = constant

  2. Compare linkage excursions

    Method

    A larger string displacement typically produces a larger flux-linkage change per cycle.

    Reason

    The magnetised string moves through a wider range of positions relative to the coil.

    Working

    |Δ(NΦ)|↑

  3. Infer signal amplitude

    Method

    The pickup e.m.f. amplitude increases.

    Reason

    A larger linkage change over the same characteristic time increases |d(NΦ)/dt|.

    Working

    |d(NΦ)/dt|↑ ⇒ |E|↑

7. Mind Stretchers

Mind stretcher 1: Stronger magnetExtension

Suggest how using a stronger pickup magnet could affect the output signal.

Show Answer

A stronger magnet increases the magnetic flux through the coil for a given string position, so the vibration can produce a larger change in flux linkage.

That can increase the induced e.m.f. amplitude.

Mind stretcher 2: Noise pickup (50/60 Hz hum)Extension

Electric guitars can pick up mains hum. Suggest one reason this can happen using induction ideas.

Show Answer

The pickup coil is a loop of wire, so changing magnetic fields from nearby mains wiring (50/60 Hz) can change flux linkage through the coil.

By Faraday’s law this induces an unwanted e.m.f. at the mains frequency (hum).

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027