Choose a method that matches the wave
Definition
Wave velocity
The distance travelled by a wavefront per unit time.
- A direct method measures distance and time, then uses v=xtv=\dfrac{x}{t}v=tx.
- An indirect method measures frequency and wavelength, then uses v=fλv=f\lambdav=fλ.
- Equipment suitability depends on wave speed, available distance and whether wavefronts can be observed or detected.
Measure sound speed electronically
- Place two microphones a measured distance apart and connect them to an oscilloscope or data logger.
- Create a short sound near the first microphone and measure the delay between the detected signals.
- Calculate v=xtv=\dfrac{x}{t}v=tx from the separation and delay.
- A larger separation reduces percentage uncertainty, while electronic timing removes human reaction time.
Example
Sound speed from a delay
- Two microphones are 1.50 m1.50\ \text{m}1.50 m apart and detect a pulse 4.4×10−3 s4.4\times10^{-3}\ \text{s}4.4×10−3 s apart.
- Use v=xtv=\dfrac{x}{t}v=tx.
- v=1.504.4×10−3=3.4×102 m/sv=\dfrac{1.50}{4.4\times10^{-3}}=3.4\times10^2\ \text{m/s}v=4.4×10−31.50=3.4×102 m/s.
Practical
Measuring waves in a fluid and a solid
- Aim: investigate the suitability of equipment for measuring wave speed, frequency and wavelength in water and in a solid.
- Water apparatus: ripple tank, shallow water, straight dipper, vibration generator, signal generator, lamp or strobe, screen, ruler and video camera or stopwatch.
- Water variables: frequency or depth is the independent variable, wave speed is calculated, and depth, temperature, dipper shape and method are controlled when comparing readings.
- Method, water:
- Level the tank, add a shallow uniform layer of water and adjust the dipper to produce clear parallel wavefronts.
- Set and record a stable frequency, using a strobe or video when crests move too quickly to observe accurately.
- Measure perpendicular to the wavefronts across at least five complete wavelengths, then divide by the number of wavelengths.
- Repeat in different positions, calculate a mean wavelength and use v=fλv=f\lambdav=fλ.
- Check by timing a wavefront over a measured distance and using v=xtv=\dfrac{x}{t}v=tx.
- Solid apparatus: long metal rod, secure clamps, vibration generator, signal generator, pickup or microphone, oscilloscope and ruler or tape measure.
- Method, solid:
- Support the rod securely and produce a steady vibration at a measured frequency.
- Use the pickup and oscilloscope, or the demonstrated resonance method, to locate repeating nodes or antinodes.
- Measure across several intervals; adjacent nodes are λ2\dfrac{\lambda}{2}2λ apart, so double the mean node spacing.
- Read the frequency and calculate v=fλv=f\lambdav=fλ, then repeat and compare values.
- Expected pattern: in a fixed medium, higher frequency gives shorter wavelength while wave speed remains approximately constant.
- Suitability: electronic frequency measurement and measurements across several wavelengths are better than hand timing for rapid waves over short distances.
- Uncertainty and improvements: avoid parallax, measure several wavelengths, use video or a strobe, repeat, calculate means, and control depth and temperature.
- Safety: mop up spills, keep electrical equipment away from water, secure the rod and apparatus, avoid sharp ends and keep sound at a safe level.
A boundary changes speed and wavelength
- When sound enters another medium, frequency stays constant because the source still oscillates at the same rate.
- Speed changes because wave speed depends on the medium.
- Since v=fλv=f\lambdav=fλ and fff is unchanged, wavelength changes in the same ratio as speed.
Common Mistake
- Do not hand-time sound over a short laboratory distance because reaction time is too large.
- Do not measure one wavelength when several can be measured and divided.
Exam technique
- Link an equipment feature to measurement quality, such as electronic timing reducing timing uncertainty.
- State each improvement and its effect on uncertainty or reliability.
Self review
- State two methods for measuring wave speed.
- Why are two microphones suitable for sound speed?
- How does measuring several wavelengths reduce uncertainty?
- What remains constant when sound enters another medium?
- State two ripple-tank safety controls.
