Wave Properties & Speed

IGCSE Edexcel Physics
3.1–3.8 Wave properties, transverse/longitudinal waves, wave speed equation and Doppler effect
Key Concepts: Waves transfer energy without transferring matter. Transverse waves: oscillations perpendicular to direction of travel. Longitudinal waves: oscillations parallel to direction of travel. $v = f\lambda$; $f = 1/T$. Doppler effect: when a source moves towards an observer the received frequency is higher than emitted; when moving away, the received frequency is lower.

Section A — Wave Definitions

1. State the difference between a transverse wave and a longitudinal wave. Give one example of each. [4]
2. Define each wave property: [4]

a) Amplitude

b) Wavelength

c) Frequency

d) Period

3. Write the equation linking frequency ($f$) and period ($T$). Calculate the frequency of a wave with period 0.04 s. [3]

Section B — Wave Speed Equation

4. Write the wave speed equation, defining all symbols and their units. [3]
5. A wave has frequency 4 Hz and wavelength 2.5 m. Calculate the wave speed. [2]
6. A sound wave has frequency 250 Hz and travels at $340\,\text{m/s}$. Calculate the wavelength. [2]
7. A radio wave has wavelength 3 m. Calculate its frequency given that all EM waves travel at $3.0 \times 10^8\,\text{m/s}$ in free space. [3]
8. A wave has period 0.2 s and wavelength 0.8 m. Calculate the wave speed. [3]

Section C — Measuring Wave Speed

9. Describe how you could measure the speed of sound in air using a starting pistol, two microphones connected to a data logger, and a known distance. [3]
10. A water wave in a ripple tank has a frequency of 5 Hz. A student measures the wavelength as 3 cm. Calculate the wave speed in m/s. [2]

Section D — The Doppler Effect

11. Explain the Doppler effect for sound. Include what happens to the observed frequency when the source moves towards and away from the observer. [3]
12. A police siren emits a constant frequency. Describe what a stationary pedestrian hears as the police car drives past them. [2]

Total marks: 34

Mark Scheme

1. Transverse: oscillations perpendicular to direction of energy transfer [1]; e.g. light/water waves [1]; Longitudinal: oscillations parallel to direction of energy transfer [1]; e.g. sound [1] [4]
2. a) Amplitude: maximum displacement from equilibrium/rest position [1]; b) Wavelength: distance between two adjacent crests (or any two identical points) [1]; c) Frequency: number of complete waves per second, measured in Hz [1]; d) Period: time for one complete wave to pass a point, measured in seconds [1] [4]
3. $f = 1/T$ [1]; $f = 1/0.04 = 25\,\text{Hz}$ [2] [3]
4. $v = f\lambda$ [1]; $v$ = wave speed (m/s), $f$ = frequency (Hz) [1], $\lambda$ = wavelength (m) [1] [3]
5. $v = f\lambda = 4 \times 2.5 = 10\,\text{m/s}$ [2]
6. $\lambda = v/f = 340/250 = 1.36\,\text{m}$ [2]
7. $f = v/\lambda = (3.0 \times 10^8)/3 = 1.0 \times 10^8\,\text{Hz}$ [3]
8. $f = 1/T = 1/0.2 = 5\,\text{Hz}$ [1]; $v = f\lambda = 5 \times 0.8 = 4\,\text{m/s}$ [2] [3]
9. Measure distance between two microphones [1]; microphone 1 starts timer when sound first arrives, microphone 2 stops it [1]; speed = distance ÷ time interval [1] [3]
10. Convert: 3 cm = 0.03 m [1]; $v = f\lambda = 5 \times 0.03 = 0.15\,\text{m/s}$ [1] [2]
11. The Doppler effect is the change in observed frequency caused by relative motion between a source and observer [1]; when the source moves towards the observer, sound waves are compressed → higher observed frequency (higher pitch) [1]; when the source moves away, waves are stretched → lower observed frequency (lower pitch) [1] [3]
12. As the car approaches, the pedestrian hears a higher pitch than the siren actually emits [1]; as the car moves away, the pitch drops and sounds lower than the actual siren frequency [1] [2]