Introduction to CP4: Speed of Sound in Air

Have you ever wondered why you see a flash of lightning before you hear the rumble of thunder? It is because sound travels much slower than light. In this core practical, we use specialized laboratory equipment to measure exactly how fast sound moves through the air. Understanding this process helps us master wave properties and prepares us for the Unit 3 (WPH13) practical skills exam.

The core of this experiment is the wave equation: \(v = f \lambda\), where \(v\) is the speed of sound, \(f\) is the frequency, and \(\lambda\) is the wavelength.

The Equipment You Need

To measure something as fast as sound (roughly \(340 \text{ m s}^{-1}\)), we cannot use a simple stopwatch. We need high-precision tools:

  • Signal Generator: This device creates an electrical signal at a specific frequency (\(f\)).
  • Loudspeaker: This converts the electrical signal from the generator into sound waves.
  • Microphone: This detects the sound waves and converts them back into an electrical signal.
  • Two-Beam Oscilloscope: This is the "brain" of the experiment. It displays two separate wave traces on a screen: one from the signal generator (the "source") and one from the microphone (the "receiver").
  • Metre Ruler: To measure the distance the microphone moves.

The Experimental Procedure

The goal is to find the wavelength (\(\lambda\)) for a known frequency (\(f\)) and then calculate the speed (\(v\)).

Step-by-Step Method:

  1. Connect the signal generator to the loudspeaker and to Channel 1 of the oscilloscope.
  2. Connect the microphone to Channel 2 of the oscilloscope.
  3. Place the microphone close to the speaker. You will see two waves on the oscilloscope screen. Adjust the oscilloscope so the two waves are in phase (the peaks and troughs of both waves line up vertically).
  4. Place a metre ruler on the bench to track the microphone's position.
  5. Slowly move the microphone away from the speaker. You will see the second wave shift on the screen.
  6. Keep moving the microphone until the two waves align perfectly again (they are back in phase). The distance the microphone has moved is equal to one wavelength (\(\lambda\)).
  7. To improve accuracy, move the microphone further so that the waves align after 10 wavelengths, then divide that total distance by 10.

Don't worry if the waves look "wiggly" or small at first! You can use the gain/volts-per-division dials on the oscilloscope to make the traces clearer.

Data Analysis and Calculations

Once you have your measurements, you can determine the speed of sound in two ways:

1. Simple Calculation

Using the frequency set on the signal generator (\(f\)) and your measured wavelength (\(\lambda\)), use the wave equation:
\(v = f \lambda\)

2. Graphical Method (More Accurate)

To reduce random errors, you should repeat the experiment for several different frequencies (e.g., \(1000 \text{ Hz}\), \(2000 \text{ Hz}\), \(3000 \text{ Hz}\)).

  • Rearrange the wave equation to: \(\lambda = v \left(\frac{1}{f}\right)\).
  • Plot a graph with wavelength (\(\lambda\)) on the y-axis and \(1/f\) on the x-axis.
  • The result should be a straight line passing through the origin.
  • The gradient of this line represents the speed of sound (\(v\)).

Quick Tip: When calculating the gradient, always use a large triangle on your best-fit line to ensure your calculation is as precise as possible.

Uncertainties and Errors

In your Unit 3 exam, you will often be asked to criticise an experimental setup or suggest improvements. Here is what to look out for in CP4:

Resolution of Instruments
  • The resolution of a standard metre ruler is \(1 \text{ mm}\) (or \(0.001 \text{ m}\)).
  • The uncertainty for a single reading is half the resolution (\(\pm 0.5 \text{ mm}\)). However, since you measure a change in distance (start and end position), the uncertainty is usually treated as \(\pm 1 \text{ mm}\).
Sources of Error
  • Systematic Error: If the waves are not perfectly aligned at the start, it could shift all readings. A "zero check" on your ruler position is vital.
  • Random Error: It can be difficult to judge exactly when the waves are perfectly "in phase" on the screen. Repeating the movement and taking a mean (average) helps reduce this.
  • Resolution Error: At very high frequencies, the wavelength is very short, making the percentage uncertainty in distance much higher.

Did you know? The speed of sound is affected by temperature. If the room gets warmer during the experiment, the air molecules move faster, and your measured value for \(v\) might increase!

Key Takeaways for Exam Success

  • The Equation: Always remember \(v = f \lambda\).
  • Phase: We move the microphone from one "in phase" position to the next to measure \(\lambda\).
  • Units: Ensure frequency is in Hertz (\(\text{Hz}\)) and distance is in metres (\(\text{m}\)) so that speed is in \(\text{m s}^{-1}\).
  • Accuracy: Measuring over 10 wavelengths instead of 1 significantly reduces the percentage uncertainty of your distance measurement.
  • Safety: Avoid setting the signal generator to very high volumes for long periods to protect your hearing and avoid disturbing others.

Note: For other core practical techniques, see CP1: Acceleration of Free Fall or CP5: Vibrating Strings.