Core Practical 6: Investigating the Speed of Sound

• The Wave Equation: The speed of sound is the product of its frequency and wavelength ($v = f\lambda$). While frequency is set by the generator, wavelength is a physical distance determined by the medium's properties.

• Time Base and Period: The oscilloscope's horizontal axis represents time. The period ($T$) is the time for one full cycle, and frequency is calculated as $f = \frac{1}{T}$.

• Spatial Phase Shift: As a microphone moves away from a sound source, the phase of the detected signal shifts relative to the source. A full $360^{\circ}$ (or $2\pi$ radians) shift indicates the microphone has moved exactly one wavelength $\lambda$.

• Step 1: Setup: Connect the signal generator to a speaker and one channel of the oscilloscope. Connect a microphone to the second channel and place it near the speaker.

• Step 2: Trace Alignment: Adjust the oscilloscope's time base and gain until both waves are clearly visible. Move the microphone until a peak on the first trace aligns with a trough on the second trace to create a clear reference point.

• Step 3: Measuring Wavelength: Move the microphone slowly away from the speaker. Count the number of times the traces return to the same relative alignment (e.g., 10 wavelengths) and record the total distance moved.

• Step 4: Frequency Verification: Use the oscilloscope's time base to measure the time period $T$ of the wave. Calculate $f = \frac{1}{T}$ rather than relying solely on the signal generator's dial for higher precision.

Measurement Comparison

• Wavelength vs. Distance: Wavelength is the distance between two consecutive points of the same phase. In the experiment, we often measure multiple wavelengths (e.g., $10\lambda$) to reduce the percentage uncertainty in the distance measurement.

• Unit Conversions: Always check the units on the oscilloscope time base. It is common to see milliseconds (ms) or microseconds ($\mu$s), which must be converted to seconds (s) before calculating frequency.

• Uncertainty Reduction: Explain that measuring the distance over several wavelengths (e.g., $d = 10\lambda$) and then dividing by 10 is superior to measuring a single wavelength because it minimizes the impact of ruler measurement errors.

• Reaction Time: If asked why this method is better than using a stopwatch and an echo, emphasize that the oscilloscope automates the timing, removing the $\approx 0.2$ s human reaction time error.

• Phase Misinterpretation: Students often mistake a $180^{\circ}$ phase shift (peak aligning with trough) for a full wavelength. A full wavelength requires the trace to return to the exact same relative position.

• Time Base Errors: Forgetting that the 'time per division' setting applies to the grid squares on the screen can lead to incorrect period calculations.

• Frequency Range: Using a frequency that is too low results in a wavelength longer than the ruler, while a frequency that is too high makes it difficult to distinguish individual cycles on the screen.