PhysicsUK

SOUND & STANDING WAVES LAB

Find the harmonics

Which frequencies make a clear stationary pattern?

0.000 s
String · fixed supports
Motion slowed to 2 drive cycles per screen second
Pickup A amplitude—
Scope frequency—
Ruler separation0.500 m

Oscilloscope

Run to fill the time window, or use Steady response.

Δt = 5.00 ms · 1 cycle → 200.0 Hz

A — solidB — dashed

Choose an investigation

Setups and up to 150 readings recover on this device. Opening a setup restarts motion paused. Kept traces remain in this tab.

Explain this experiment

Read the picture

Try the investigation

    Change
    Keep the same
    Record
    Read the instruments

    In Voltage–time, the scope's horizontal axis is elapsed physical time in milliseconds. There are 10 horizontal divisions; 1 ms = 0.001 s. The vertical axis is voltage, with 8 divisions. View gain and slow motion change the picture, not these measurements.

    For a repeating trace, Freeze trace, place the cursors on equivalent points (such as two upward zero crossings), and count the complete cycles between them. With N cycles in time Δt, period T = Δt / N and frequency f = N / Δt. The cursor calculation assumes your cycle count is correct. A single pulse has no repeating period.

    Amplitude is half the peak-to-peak voltage in the displayed window. A reading of 0.000 V means a measured signal is very small; — means the measurement is unavailable. A node can give a flat trace even while other parts of the medium move. Move A, check its connection, or increase the time-base if a frequency cannot be measured.

    Capture reading stores the values and apparatus settings in Notebook. Keep trace stores a comparison waveform in this tab; comparison traces appear in Voltage–time when their time windows match. Spectrum shows the frequencies present in A; its vertical scale adjusts automatically. A pluck can have several peaks, while a settled continuous drive oscillates at the drive frequency.

    Explain the result

    A harmonic is a whole-number multiple of the fundamental frequency. A resonance is a large response when the driving frequency is close to a natural frequency. Driving a system does not automatically mean it is at resonance.

    What the buttons do
    Run / Pause and Step
    Advance or pause physical time. Step advances a small interval and leaves motion paused. Run alone does not pluck a string or launch a pulse.
    Steady response
    Calculate the continuously driven response after transients have died away. This needs a connected driver inside the medium. It preserves the current Run/Pause choice, so press Run if you want to animate the calculated shape.
    Pluck
    Drag the green string up or down and release, or use Pluck at the selected position. Release starts free vibration from the held triangular shape and turns off continuous forcing. Pull farther for greater amplitude; choose another point to change the mixture of harmonics. Escape cancels a pull. No powered driver is required.
    Send pulse
    Launch a pulse from the left. Restart between comparisons, or send several pulses to investigate overlap.
    Restart
    Clear the motion and pause, keeping the apparatus and notebook. After Restart, use Pluck or Send pulse again if appropriate.
    Freeze trace / Resume trace
    Hold or release the scope display. Freezing the trace does not pause the apparatus. Capture while frozen uses the frozen trace and its saved settings.
    Handles and precise controls
    Drag labelled handles along the bench. Focus a handle and use left/right arrows for 0.01 m steps; Shift gives larger 0.05 m steps. Apparatus offers exact positions in metres. Moving the Pluck handle chooses where the next pluck occurs.
    Listen
    Play a quiet, uncalibrated sonification at physical pitch while the animation stays slow. The microphones on the bench are simulated; your device microphone is not used.
    Model assumptions and course level

    The string is uniform and its supports are ideal. The driver applies a transverse force near a support. Air columns have ideal open or rigid closed ends, with no end correction or sound radiation model. A finite set of 16 damped modes describes vibration. Frequencies above this range are marked unavailable. Air dots are tracers of fluid elements, not individual molecules; their rest spacing stays fixed when the tube is resized. Motion is enlarged and slowed; instruments use physical units. The reflection bench shows a pulse's first reflection; the source end absorbs its return.

    GCSE exploration covers wave quantities and sound. Quantitative harmonics, string tension and resonance-tube work are A-level investigations. AQA uses “first harmonic”; OCR also uses “fundamental”.

    Editable apparatus

    Add or remove parts, then connect the source and instruments. Drag the labelled handles on the bench, or use the position controls here.

    Length, string replacement and boundary changes restart the wave field. Particles, probes, driver and ruler keep their physical positions; move an out-of-range probe back inside the medium. Frequency, force, tension, damping and probe changes work live. Undo restores apparatus settings; it does not reverse elapsed motion.

    Experiment controls

    Instrument calibration and limitations

    Damping controls how quickly free vibration fades. A larger damping ratio also lowers and broadens a resonance peak. Drive strength sets the relative forcing, rather than electrical power in watts. Change one at a time when comparing amplitudes.

    A string pickup produces 0.500 V per mm of local displacement. The virtual microphone produces 0.500 V per Pa of local pressure variation. These are declared ideal transducers. Device loudness and Listen volume are not calibrated sound-pressure levels.

    Scope frequency comes from rising crossings of its sampled trace. A node, a short time window or a mixed waveform may prevent a useful frequency reading. Use cursors across several cycles. The spectrum uses a Hann window; closely spaced peaks need a longer time window.

    Steady response solves the settled, continuously driven state directly. Run shows the damped response from the current state. Changing a live parameter preserves modal displacement and velocity. Listen sonifies the current modal frequencies at audible pitch; it does not simulate the sound radiation of a string.

    Investigation notebook

    The fit uses the latest compatible series and needs three different x values. Other series remain visible in different colours. Frequencies at nodes are unavailable.

    # Bench Length / m Drive / Hz Amplitude / V Measured / Hz Ruler / m Note

    Kept traces