P21: Wave Properties
Transverse and longitudinal waves, wave speed calculations
Wave Properties
📋 Key Definitions
Wave: Vibrations that transfer energy from one place to another without transferring matter. The substance a wave travels through is called the medium.
Transverse wave: A wave where the vibrations are perpendicular (at right angles) to the direction of energy transfer.
Longitudinal wave: A wave where the vibrations are parallel to the direction of energy transfer.
Amplitude: The maximum displacement of a wave from its rest position. Larger amplitude = more energy.
Wavelength (λ): The distance between the same point on two adjacent waves (e.g. crest to crest or trough to trough). Measured in metres.
Frequency (f): The number of waves passing a point per second. Measured in hertz (Hz). 1 Hz = 1 wave per second.
Period (T): The time taken for one complete wave to pass a point. Measured in seconds.
📝 Types of Waves
Transverse Waves
In transverse waves, the vibrations are perpendicular to the direction of energy transfer. Imagine shaking a rope up and down — the wave travels along the rope but the rope moves up and down.
- Electromagnetic waves (light, radio, X-rays etc.)
- Water ripples
- Waves on a stretched rope or string
- S-waves (secondary seismic waves)
Longitudinal Waves
In longitudinal waves, the vibrations are parallel to the direction of energy transfer. They consist of compressions (regions of high pressure) and rarefactions (regions of low pressure).
- Sound waves in air, liquids and solids
- P-waves (primary seismic waves)
- Ultrasound
| Property | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Vibration direction | Perpendicular to direction of travel | Parallel to direction of travel |
| Can travel in vacuum | EM waves can; mechanical ones cannot | Cannot (need a medium) |
| Features | Crests (peaks) and troughs | Compressions and rarefactions |
| Examples | Light, water ripples, rope waves | Sound waves, P-waves |
📐 Wave Equations
Wave speed: v = f × λ
v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)
v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)
Period: T = 1 / f
T = period (s), f = frequency (Hz)
T = period (s), f = frequency (Hz)
These equations are on the equation sheet but you must know how to rearrange them.
🔬 Required Practical: Measuring Wave Speed
Method 1: Ripple Tank
Ripple Tank Method: Use a ripple tank to produce water waves. Measure the wavelength using the shadow pattern on the screen below the tank (measure across several waves then divide). Measure the frequency by counting waves passing a point in a set time. Then calculate v = f × λ.
- Set up the ripple tank with a vibrating bar to produce straight waves.
- Use a strobe light to make the waves appear stationary on the screen below.
- Measure the distance between several wave crests and divide by the number of wavelengths to find λ.
- Count the number of waves passing a point in 10 seconds and divide by 10 to find f.
- Calculate v = f × λ.
Method 2: Stretched String and Vibration Generator
String Method: Attach a string to a vibration generator and a pulley with a hanging mass. Adjust the frequency until a clear standing wave forms. Measure the wavelength of the standing wave and read the frequency from the signal generator. Calculate v = f × λ.
- Connect a vibration generator to a signal generator.
- Attach a piece of string to the vibration generator, pass it over a pulley and attach a mass to the end.
- Turn on the signal generator and adjust the frequency until a clear standing wave is visible.
- Measure the wavelength (distance between adjacent nodes × 2 gives λ).
- Record the frequency from the signal generator.
- Calculate v = f × λ.
🧮 Worked Examples
Example 1: Calculating wave speed
A wave has a frequency of 50 Hz and a wavelength of 0.6 m. Calculate the wave speed.
Solution:
v = f × λ = 50 × 0.6 = 30 m/s
Example 2: Calculating wavelength
A sound wave travels at 330 m/s with a frequency of 440 Hz. Calculate the wavelength.
Solution:
λ = v ÷ f = 330 ÷ 440 = 0.75 m
Example 3: Calculating frequency
A water wave travels at 1.5 m/s with a wavelength of 0.3 m. Calculate the frequency.
Solution:
f = v ÷ λ = 1.5 ÷ 0.3 = 5 Hz
Example 4: Calculating period
A wave has a frequency of 200 Hz. Calculate its period.
Solution:
T = 1 ÷ f = 1 ÷ 200 = 0.005 s (or 5 ms)
Example 5: Ripple tank calculation
In a ripple tank, a student measures 5 wavelengths across a distance of 12 cm. The frequency of the vibrator is 4 Hz. Calculate the wave speed.
Solution:
Step 1: Find wavelength — λ = 12 cm ÷ 5 = 2.4 cm = 0.024 m
Step 2: Calculate speed — v = f × λ = 4 × 0.024 = 0.096 m/s
Example 6: Unit conversion
A radio wave has a frequency of 900 MHz and travels at 3 × 10⁸ m/s. Calculate its wavelength.
Solution:
f = 900 MHz = 900 × 10⁶ Hz = 9 × 10⁸ Hz
λ = v ÷ f = 3 × 10⁸ ÷ 9 × 10⁸ = 0.333 m (or 33.3 cm)
❓ Practice Questions
Q1: Foundation A wave has a frequency of 20 Hz and a wavelength of 0.5 m. Calculate its wave speed.
Q2: Foundation A sound wave travels at 340 m/s and has a frequency of 680 Hz. Calculate its wavelength.
Q3: Higher A wave has a period of 0.025 s. Calculate its frequency.
Q4: Higher Describe the difference between a transverse wave and a longitudinal wave. Give one example of each.
Q5: Foundation A student measures 8 complete wavelengths in a ripple tank over a distance of 48 cm. The frequency is 5 Hz. Calculate the wave speed.
Q6: Higher Explain how you would measure the speed of water waves using a ripple tank.
✅ Answers
- Q1: v = f × λ = 20 × 0.5 = 10 m/s
- Q2: λ = v ÷ f = 340 ÷ 680 = 0.5 m
- Q3: f = 1 ÷ T = 1 ÷ 0.025 = 40 Hz
- Q4: In a transverse wave, vibrations are perpendicular to the direction of energy transfer (e.g. light waves). In a longitudinal wave, vibrations are parallel to the direction of energy transfer (e.g. sound waves). Transverse waves have crests and troughs; longitudinal waves have compressions and rarefactions.
- Q5: λ = 48 cm ÷ 8 = 6 cm = 0.06 m. v = f × λ = 5 × 0.06 = 0.3 m/s
- Q6: Set up the ripple tank with a vibrating bar to produce straight waves. Use a strobe light or mark a point on the screen below. Measure the wavelength by measuring across several wave shadows and dividing by the number of wavelengths. Measure the frequency by counting the number of waves passing a point in a set time (or read from the signal generator). Then calculate wave speed using v = f × λ.
🎯 Exam Tips
- Always check units — convert cm to m, kHz to Hz (×1000), MHz to Hz (×10⁶) before calculating.
- Remember: waves transfer energy, NOT matter. The particles just vibrate about their rest position.
- When describing wave types, always state the direction of vibrations relative to the direction of energy transfer.
- For the ripple tank practical, remember to measure multiple wavelengths then divide — this reduces uncertainty.
- Frequency is measured in Hz (not 'cycles per second' in exams).
- The period equation T = 1/f can be rearranged to f = 1/T if you need frequency from period.
🔬 Required Practical
Required Practical: Investigating Waves on a String and in a Ripple Tank
Aim: To measure the frequency and wavelength of waves and use v = f × λ to calculate the wave speed.
Method (Ripple Tank): 1) Set up a ripple tank with a vibrating bar to produce straight water waves. 2) Use a strobe light to make the waves appear stationary on the screen below. 3) Measure the distance across several wavelengths and divide by the number of waves to find λ. 4) Count the number of waves passing a fixed point in 10 seconds and divide by 10 to find f. 5) Calculate v = f × λ.
Method (Stretched String): 1) Connect a vibration generator to a signal generator and attach a string over a pulley with a hanging mass. 2) Adjust the frequency until a clear standing wave forms. 3) Measure the wavelength (distance between adjacent nodes × 2). 4) Read the frequency from the signal generator. 5) Calculate v = f × λ.
Variables: IV: frequency of vibration generator, DV: wavelength of the wave, Control: tension in the string / depth of water in ripple tank
🔢 Maths Skills
Mathematical Skills
Rearranging the wave speed equation v = f × λ. You may need to find any one of the three variables. Always convert units before calculating: cm → m (÷100), kHz → Hz (×1000), MHz → Hz (×1,000,000). Also use T = 1/f to convert between period and frequency.
Maths Example
A wave has a wavelength of 8 cm and a period of 0.02 s. Calculate the wave speed. Step 1: Convert wavelength — λ = 8 cm = 0.08 m. Step 2: Find frequency — f = 1/T = 1/0.02 = 50 Hz. Step 3: Calculate speed — v = f × λ = 50 × 0.08 = 4 m/s.
⚠️ Common Misconceptions
Watch Out!
1. Wrong: Waves transfer matter from one place to another Correct: Waves transfer energy, not matter — particles simply vibrate about their rest position
2. Wrong: A higher amplitude means a higher frequency Correct: Amplitude and frequency are independent — amplitude affects energy/loudness, frequency affects pitch
3. Wrong: Sound waves are transverse because they spread out in all directions Correct: Sound waves are longitudinal — the particles vibrate parallel to the direction of energy transfer, creating compressions and rarefactions
✍️ 6-Mark Question
Extended Answer
6 marks: Describe how you would measure the speed of water waves in a ripple tank. Explain how your method reduces uncertainty in the result.
Set up a ripple tank with a vibrating bar to produce straight waves and a strobe light below. Measure the wavelength by placing a ruler on the screen below the tank and measuring across several wave crests (e.g. 5 wavelengths), then dividing the total distance by the number of wavelengths. This reduces uncertainty compared to measuring a single wavelength. Measure the frequency by counting the number of waves passing a fixed point in 10 seconds and dividing by 10. Counting over a longer time reduces timing uncertainty. Alternatively, read the frequency directly from the signal generator connected to the vibrator. Finally, calculate the wave speed using v = f × λ. Repeat the measurements and calculate a mean to improve reliability.
Mark scheme: 1 mark — use ripple tank with vibrating bar, 1 mark — measure multiple wavelengths and divide to find λ (reduces uncertainty), 1 mark — measure frequency by counting waves over a set time or reading from signal generator, 1 mark — calculate v = f × λ, 1 mark — explain why measuring multiple wavelengths reduces uncertainty, 1 mark — repeat measurements and calculate mean
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student measures the wave speed in a ripple tank using two different methods. Method A gives v = 0.12 m/s. Method B (using a vibration generator and string) gives v = 0.15 m/s. The accepted value is 0.14 m/s.
(a) Calculate the percentage error for each method.
(b) Which method gave the more accurate result? Explain your answer.
(c) The student measured 4 wavelengths across 10 cm in Method A. Suggest how they could improve the reliability of this measurement.
Answers: (a) Method A: (0.14 − 0.12)/0.14 × 100 = 14.3%. Method B: (0.15 − 0.14)/0.14 × 100 = 7.1%. (b) Method B is more accurate because its percentage error is smaller (7.1% vs 14.3%). (c) Measure across more wavelengths (e.g. 8 or 10) to reduce the uncertainty in each individual wavelength measurement, and repeat several times to calculate a mean.
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