Core Practical 4: Investigating the Speed of Sound

Wave Equation Foundation: The speed of sound is constant in a uniform medium at a specific temperature. Therefore, the relationship $v = f\lambda$ implies that if the frequency is increased, the wavelength must decrease proportionally to maintain the constant speed.

Phase and Path Difference: As the microphone moves away from the speaker, the time taken for the sound wave to reach it increases. This time delay manifests as a phase shift on the oscilloscope; a distance change of exactly one wavelength corresponds to a phase shift of $360^\circ$ or $2\pi$ radians.

Frequency Determination: Frequency is calculated using the time base of the oscilloscope rather than the signal generator dial. By measuring the time period ($T$) for one complete cycle on the screen, the frequency is derived as $f = \frac{1}{T}$.

Initial Setup: Connect the signal generator to one input of a dual-beam oscilloscope and the microphone to the second input. Place the microphone approximately 50 cm from the speaker and set the frequency to a clear, audible range such as 4 kHz.

Trace Alignment: Adjust the oscilloscope settings so that both waves are visible. It is often easier to align a peak of the source signal with a trough of the received signal, as the point of intersection is visually distinct and easier to track than two peaks.

Measuring Wavelength: Move the microphone slowly away from the speaker while watching the traces. Record the distance moved between consecutive points where the traces return to the same relative alignment; this distance is equal to one wavelength $\lambda$.

Data Collection: Repeat the process for several wavelengths to find a mean value for $\lambda$. Additionally, repeat the entire experiment at a different frequency (e.g., 2 kHz) to verify the consistency of the calculated speed of sound.

Oscilloscope vs. Signal Generator: The frequency should always be determined from the oscilloscope trace ($f = \frac{1}{T}$) rather than the signal generator dial. Signal generator dials are often approximate and uncalibrated, whereas the oscilloscope's time base provides a direct measurement of the signal being analyzed.

Phase Alignment vs. Peak Matching: While aligning peaks is intuitive, aligning a peak with a trough is often more precise. This is because the human eye is better at detecting the exact point where a rising curve crosses a falling curve than identifying the exact 'flat' top of a peak.

Unit Conversions: Always check the units on the oscilloscope time base. It is common for the scale to be in milliseconds (ms) or microseconds ($\mu$s); failing to convert these to seconds will result in frequency values that are incorrect by factors of 1,000 or 1,000,000.

Accuracy Justification: If asked why this method is accurate, focus on the elimination of human reaction time. Because the oscilloscope handles the timing of the wave cycles electronically, the uncertainty is limited only by the calibration of the equipment and the precision of the distance measurement.

Sanity Checks: The speed of sound in air is approximately $330$ to $345 \text{ m/s}$. If your calculated value is significantly different (e.g., $3.4 \text{ m/s}$ or $34,000 \text{ m/s}$), re-examine your unit conversions for distance (cm to m) and time (ms to s).

Confusing Distance with Wavelength: Students often record the total distance from the speaker rather than the change in distance between phase alignments. Only the distance moved between identical phase points represents the wavelength $\lambda$.

Parallax Error: When measuring the position of the microphone against a ruler, looking at an angle can lead to incorrect distance readings. Ensure the measurement is taken at eye level directly above the microphone's reference point.

Ignoring Background Noise: High levels of ambient noise can cause the received signal on the oscilloscope to appear 'fuzzy' or unstable. This makes it difficult to judge the exact point of phase alignment, increasing the uncertainty of the wavelength measurement.