Measuring Wave Speed & Required Practical 8

When the signal generator is turned on, waves travel down the string and reflect back, superposing to form a standing wave. This pattern features nodes, which are points with zero displacement, and antinodes, which are points with maximum displacement.

Read the frequency directly from the signal generator. Measure the total length of multiple visible loops using a ruler; one loop (the distance between two adjacent nodes) represents exactly half a wavelength ($\frac{1}{2}\lambda$). Calculate the full wavelength, then multiply by the frequency to find the speed.

Worked Example

Calculations require precision. A student measures the total length of 3 loops as $0.215\text{ m}$. The frequency is $15\text{ Hz}$. Calculate the wave speed.

Step 1: Calculate the length of one loop.

• Length of 1 loop = $0.215 / 3 = 0.0717\text{ m}$

Step 2: Calculate the full wavelength ($\lambda$).

• $\lambda = 0.0717 \times 2 = 0.1434\text{ m}$

Step 3: Substitute into the wave equation ($v = f \lambda$).

• $v = 15 \times 0.1434$
• $v = 2.15\text{ m/s}$

Measuring the Speed of Sound in Air: Oscilloscope Method

Lightning and thunder happen at exactly the same time, but why do you always see the flash before you hear the boom? Sound travels fast, but we can measure its exact speed using high-frequency sound waves (e.g., $4\text{ kHz}$) and two microphones connected to a dual-trace oscilloscope.

First, place both microphones in front of a loudspeaker so their traces align on the screen, meaning they are in phase. Then, move one microphone away from the speaker until the two traces align exactly once more. The distance between the microphones is exactly one wavelength.

Alternatively, you can place the microphones at a known distance and use the oscilloscope's timebase to measure the time delay for a sound pulse to travel between them. The speed is then calculated by dividing the distance by the time delay.

Measuring the Speed of Sound in Air: Echo Method

Shouting into a canyon and hearing your voice bounce back is a classic example of an echo. To use echoes to measure the speed of sound, stand at least 50 metres from a tall, vertical wall. Measure this distance using a trundle wheel, as it is far more practical than a standard metre ruler over long distances.

A person claps two wooden blocks together in rhythm with the echoes they hear returning from the wall. A second person uses a stopwatch to time a large number of claps (e.g., 50 or 100 claps) to calculate the total time taken.

Worked Example

A student stands $50\text{ m}$ from a wall. They time 20 claps. The total time taken is $6.1\text{ s}$. Calculate the speed of sound.

Step 1: Calculate the total distance. Remember sound travels to the wall AND back for every clap.

• Total distance = $2 \times 50 \times 20 = 2000\text{ m}$

Step 2: Use the speed formula ($v = \frac{d}{t}$).

• $v = \frac{2000}{6.1}$
• $v = 327.9\text{ m/s}$

Evaluating Apparatus Suitability

Would you use a plastic ruler to measure the thickness of a human hair? Choosing the right tool is vital in physics to ensure reliable results and low uncertainty.

A standard stopwatch has a resolution of $0.01\text{ s}$, but human reaction time is typically $0.2\text{ s}$ to $0.9\text{ s}$. This introduces significant random error for fast events like sound traveling short distances. An oscilloscope is highly suitable here because its microsecond resolution entirely eliminates human reaction time.

For ripple tanks, recording a slow-motion video with a timer in the frame allows for frame-by-frame analysis. This massively reduces systematic observation errors compared to manual counting. In all methods, measuring across multiple waves (10 wavefronts or 10 loops) is the best way to reduce the percentage uncertainty of the final result.