CP4 – Speed of Sound | Edexcel A Level Physics

Theory & Background

Speed of sound, phase difference and the cathode ray oscilloscope

Objectives

Determine the speed of sound in air using a signal generator, speaker and microphone connected to a 2-beam CRO
Understand how sound travels as a longitudinal pressure wave and measure its speed using v = d/t
Use the CRO timebase to measure the time delay between CH1 (speaker signal) and CH2 (microphone signal)
Plot a graph of distance d against time delay t and determine v from the gradient

The Physics

A signal generator produces an alternating voltage at a set frequency f. This drives a loudspeaker, creating a sound wave in air. A microphone converts the sound pressure wave back into an electrical signal. Because sound travels at a finite speed v, the microphone signal lags behind the speaker signal by a time delay t:

v = d / t ∴ d = v · t

d = distance from speaker to microphone (m), measured with a metre rule
t = time delay between CH1 and CH2 signals (s), read from the CRO
v = speed of sound in air ≈ 343 m/s at 20°C

Plotting d (y-axis) against t (x-axis) gives a straight line through the origin. The gradient equals v — the speed of sound.

Reading the CRO

The CRO displays voltage (y-axis) against time (x-axis). The timebase setting controls how many milliseconds each horizontal division represents. To find the time delay:

Time delay t = (number of divisions between peaks) × (time/div setting)

Example: peaks separated by 2.3 divisions, timebase = 0.5 ms/div → t = 2.3 × 0.5 = 1.15 ms = 1.15 × 10⁻³ s

The key skill is choosing the right timebase — too slow and you can't see the phase shift clearly; too fast and you only see part of one wave cycle.

Important Considerations

Use a frequency of 1–4 kHz — the wavelength is 8–34 cm, large enough to see phase shifts over practical distances
Move the microphone in one direction only — back and forth movement introduces parallax error in distance measurement
Avoid reflections — carry out the experiment away from walls, or use sound-absorbing material behind the microphone
Temperature affects v — note the room temperature and compare with v = 331 + 0.6T (m/s) where T is in °C

CRO Basics — Learn the Oscilloscope

Master the controls before starting the experiment. Work through the guided tutorial or explore freely.

Tutorial — Step 1 of 8

Welcome to the CRO (Cathode Ray Oscilloscope). Press the POWER button on the right panel to switch it on. You should see a flat green line appear on the screen.

💡 In a real CRO, warming up takes a few seconds before the beam appears.

        ■ CH1 (Y1)
        Timebase: 0.5 ms/div
        ■ CH2 (Y2)
      

Power

Channel Input

Input Coupling

TIME/DIV

0.5 ms

click to cycle

VOLTS/DIV

1.0 V

click to cycle

Trigger

Acquisition

Press to freeze trace for reading

Y-Position

CH1 ↕

CH2 ↕

Test Signal (CRO practice)

Test freq 1000 Hz

CH2 phase shift 90°

Measurements
CH1 freq: —
CH1 period: —
CH2 delay: —
÷ div: —

Step-by-Step Procedure

Follow these steps carefully in the Simulation tab

Equipment

Signal generator · Loudspeaker · Microphone · 2-beam CRO (or data logger with oscilloscope function) · Metre rule · Connecting leads

Set up the signal generator and CRO

Connect the signal generator output to CH1 of the CRO and also to the loudspeaker. Connect the microphone output to CH2. Set the signal generator to 2–4 kHz. Set the CRO to DUAL mode so both traces are visible.

Choose the timebase setting

Select a timebase that shows 2–3 complete wave cycles on screen. For 2 kHz (period = 0.5 ms), a timebase of 0.1–0.2 ms/div works well. You should clearly see two separate sinusoidal traces.

Period T = 1/f → 2 kHz: T = 0.5 ms → use 0.1 ms/div

Position microphone at initial distance d

Place the microphone close to the speaker (~10 cm). Use the distance slider. Note the phase shift between the two traces — CH2 should lag behind CH1.

Measure the time delay t from the CRO

Count the number of horizontal divisions between corresponding points (e.g. peak to peak) on CH1 and CH2. Multiply by the timebase setting to get the time delay t.

t = divisions × time/div e.g. 1.8 div × 0.1 ms/div = 0.18 ms

Record the reading

Click Record Reading. The simulation logs d and t. Move the microphone to a new distance and repeat. Collect at least 6 readings across a range of 10–80 cm.

Plot d vs t and find v

Go to the Graph tab. Plot distance d (y-axis) against time delay t (x-axis). The gradient of the best-fit line equals the speed of sound v.

v = gradient of d–t graph (m/s)

Experiment Controls

Signal frequency f 2000 Hz

500 Hz5000 Hz

Microphone distance d 0.20 m

0.05 m1.00 m

CRO Timebase 0.2 ms/div

Acquisition

Freeze the CRO to count divisions

Room temperature 20 °C

0°C40°C

Distance d

—

Time delay t

—

Divisions

—

v = d/t

—

Readings recorded: 0/6 minimum

Live CRO Display — DUAL mode

      ■ CH1 — Speaker (reference)
      ■ CH2 — Microphone (delayed)
      ↔ measure divisions between peaks
    

Results Data Table

Auto-filled from simulation. You need ≥6 readings at different distances for a reliable graph.

#	d/ m	t (CRO)/ ms	t/ s	Divisionscounted	Timebasems/div	v = d/t/ m s⁻¹
No data yet — go to Simulation tab.

Graph & Analysis

Plot of distance d (y-axis) against time delay t (x-axis). Gradient = speed of sound v.

Speed of Sound

—Record ≥3 readings first

Graph Parameters

Gradient v—

R²—

Expected v (temp)—

% Difference—

Temperature Correction

Room temp T—

v = 331 + 0.6T—

Speed of sound increases by ~0.6 m/s per °C rise in temperature.

Interpretation

Complete your experiment to see analysis.

Discussion Questions

Write your answers and reveal model answers when ready.

Question 1

Explain why the microphone signal (CH2) appears to lag behind the speaker signal (CH1) on the CRO display.

Sound travels at a finite speed (~343 m/s) through air. The signal generator produces the electrical signal simultaneously driving both CH1 and the speaker. The speaker converts this to a sound wave, which travels through the air to the microphone. The time taken for sound to travel from speaker to microphone introduces a time delay t = d/v. This delay causes the CH2 waveform to appear shifted to the right of CH1 on the CRO screen — the greater the distance d, the larger the phase shift observed.

Question 2

Describe how you would choose an appropriate timebase setting for this experiment when using a signal frequency of 3 kHz.

At 3 kHz, the period T = 1/f = 1/3000 = 0.333 ms. To display 2–3 complete cycles across 10 divisions, each division should represent about T/10 × 3 ≈ 0.1 ms. Therefore a timebase of 0.1 ms/div is appropriate. This gives 3.33 cycles across the screen — enough to clearly see the phase shift between CH1 and CH2 while still showing multiple cycles. A timebase that is too slow (e.g. 1 ms/div) would compress too many cycles together, making it hard to measure divisions accurately. A timebase that is too fast (e.g. 0.01 ms/div) would show only a small fraction of a cycle.

Question 3

Explain why plotting d against t gives a straight line through the origin, and why the gradient equals the speed of sound.

From v = d/t, rearranging gives d = v·t. This is of the form y = mx where m = v is constant (the speed of sound is constant at a fixed temperature). Therefore d is directly proportional to t, giving a straight line through the origin. The gradient m = Δd/Δt = v, the speed of sound. The line passes through the origin because when d = 0 (microphone at speaker), there is zero time delay. Any non-zero intercept would indicate a systematic error, such as a fixed electrical delay in the equipment.

Question 4

The speed of sound in air varies with temperature according to v = 331 + 0.6T m/s. Suggest how you could use this to improve the accuracy of your experiment.

Measure the room temperature T with a thermometer and calculate the expected speed of sound using v = 331 + 0.6T. Compare this with your measured gradient. If the percentage difference is small (e.g. <3%), this validates your result. To improve accuracy: (1) Carry out the experiment at a known stable temperature and use the formula to correct the expected value. (2) Repeat the experiment at different temperatures and plot v against T — the gradient should be 0.6 m/s/°C and the intercept 331 m/s. (3) Avoid draughts and temperature gradients in the room, which would cause v to vary along the path.

Question 5

Suggest two sources of error specific to this experiment and explain how each would affect your measured value of v.

1. Reflections from walls — reflected sound waves arrive at the microphone slightly after the direct wave, creating a superposition that distorts the waveform and makes it harder to identify the peak position accurately. This introduces a random error in reading t, increasing the scatter on the d–t graph. To reduce this, use a room with sound-absorbing walls, or place absorbing material behind the microphone. 2. Difficulty reading divisions on the CRO — estimating the number of divisions between peaks introduces uncertainty. Reading to the nearest 0.1 division over 2 divisions gives a 5% uncertainty in t and therefore in v. Using cursor functions on a digital oscilloscope, or taking the reading at multiple frequencies and averaging, would reduce this uncertainty.