Know that the speed of sound in air is approximately 330-350 m/s

Relationship Between Speed, Frequency and Wavelength (useful bridge – not required for core AO1)

For any wave, v = fλ. Example: a 1 kHz tone in air at 20 °C has a wavelength λ = v/f ≈ 343 m s⁻¹ / 1000 Hz ≈ 0.34 m.

Factors Influencing the Speed in Air (AO2)

• Temperature: Higher temperature → faster molecular motion → shorter time between collisions → larger v.
• Medium (state of matter): Solids and liquids have particles closer together and a larger bulk modulus, so sound travels faster than in gases.
• Humidity: Water‑vapour molecules are lighter than N₂/O₂; increased humidity slightly raises v.
• Air pressure: At constant temperature, pressure changes density and bulk modulus proportionally, giving a negligible net effect on v.

Why Speed Differs in Different Media (AO2)

Longitudinal wave speed is given by

v = √(B/ρ)

where B is the bulk modulus (rigidity) and ρ is the density. Solids have a large B and moderate ρ, giving a high speed; gases have a small B and low ρ, giving a low speed.

Typical Speeds (AO1)

Measuring the Speed of Sound in Air (AO3)

1. Apparatus: two microphones (or two pressure‑sensitive transducers), a rigid stand to fix them a known distance d apart (e.g., 2.00 m), a short‑duration sound source (clap, popped balloon), oscilloscope or digital timer, thermometer.
2. Set‑up sketch: (see diagram at the end). Mark the distance d clearly.
3. Procedure
   1. Place the sound source close to the first microphone.
   2. Trigger the source and record the time of arrival at each microphone (t₁ and t₂).
   3. Calculate the time interval Δt = t₂ – t₁.
   4. Compute the speed for that trial: v = d / Δt.
   5. Repeat the measurement at least three times.
4. Data table (example)

   Trial	Δt (s)	v (m s⁻¹)	Comment
   1
   2
   3

5. Analysis
   • Calculate the mean speed v̄ and the percentage uncertainty (Δv / v̄) × 100 %.
   • Compare the experimental value with the theoretical 330–350 m s⁻¹ range.

Example Calculation (single trial)

Given d = 2.00 m and a measured Δt = 0.0059 s:

v = 2.00 m / 0.0059 s ≈ 339 m s⁻¹

Repeating three trials might give 0.0059 s, 0.0058 s and 0.0060 s, yielding a mean v̄ ≈ 340 m s⁻¹ with a small uncertainty, comfortably within the syllabus range.

Common Sources of Error (AO3)

• Inaccurate measurement of the distance d (parallax, ruler error).
• Electronic delay in the detection circuitry (trigger lag) – tends to over‑estimate Δt.
• Temperature change during the experiment – record the temperature and apply the correction formula v = 331 + 0.6 T.
• Reflections from nearby walls or objects producing secondary pulses that may be mistaken for the direct arrival.

Uses of Ultrasound (Supplementary Content – optional AO2)

• Medical imaging (e.g., obstetric scans) – high‑frequency sound (> 1 MHz) is reflected from tissue interfaces; the time‑of‑flight of the echoes produces an image of internal structures.
• Non‑destructive testing (NDT) of metals – ultrasonic pulses are sent into a metal part; reflections from cracks or voids are detected and analysed to locate defects.
• Sonar for navigation and depth measurement – underwater ultrasonic pulses travel through water, reflect from the seabed or objects, and the return time gives distance.

All these applications rely on the same principle: **reflection of high‑frequency sound** from boundaries where acoustic impedance changes.

Key Points to Remember (AO1 Summary)

• Accepted approximate speed of sound in air: ≈ 330 – 350 m s⁻¹** at 20 °C.
• Sound is a longitudinal wave consisting of alternating compressions and rarefactions.
• Human hearing range: 20 Hz – 20 kHz; pitch ↔ frequency, loudness ↔ amplitude.
• Sound cannot travel in a vacuum – an elastic medium is essential.
• Temperature is the dominant factor affecting speed in air; humidity has a small effect; pressure is negligible.
• Speed increases with the rigidity of the medium (solids > liquids > gases) because v = √(B/ρ).
• Ultrasound (> 20 kHz) is used in medicine, industry and marine navigation, all based on sound‑wave reflection.
• Accurate measurement of v requires careful control of distance, timing, temperature, and a systematic recording and evaluation of data.