Measuring waves

To find the wave speed using the formula $v = f \lambda$, you must measure both the Wavelength (λ) and the Frequency (f):

• Wavelength (λ): First, place a metre ruler on the screen. Then, measure the distance across a large number of wave shadows (for example, 10 waves). Finally, divide this total distance by the number of waves to find the length of a single wave.
• Frequency (f): First, pick a fixed point on the screen. Then, use a stopwatch to time how many waves pass that exact point in 10 seconds. Finally, divide the total number of waves by 10 to find the number of waves per second. Alternatively, a flashing stroboscope can be matched to the frequency of the waves until they appear to "freeze", allowing you to read the frequency directly.

Worked Example: Ripple Tank Calculation

A student uses a ripple tank to investigate water waves. They measure the distance across 8 complete waves to be $0.24\text{ m}$. They count 12 waves passing a fixed mark in $10\\text{ s}$. Calculate the speed of the water waves.

Step 1: Calculate the wavelength ($\lambda$).

• $\lambda = 0.24\text{ m} \div 8 = 0.03\text{ m}$

Step 2: Calculate the frequency ($f$).

• $f = 12 \text{ waves} \div 10\text{ s} = 1.2\text{ Hz}$

Step 3: Use the wave equation to calculate speed ($v$).

• $v = 1.2\text{ Hz} \times 0.03\text{ m}$
• $v = 0.036\text{ m/s}$

Measuring the Speed of Sound (Echo Method)

Shouting into a vast canyon and waiting for your voice to bounce back is more than just fun—it is the basis for a classic physics experiment. The speed of sound in air can be measured by calculating how long it takes for an echo to travel over a known distance.

First, stand a long distance away (typically $50\text{ m}$ or $100\text{ m}$) from a tall, flat wall. Measure this distance precisely using a trundle wheel. Next, one person strikes two wooden blocks together to create a sharp, loud sound. A second person stands alongside them holding a stopwatch. Because light travels much faster than sound, the timer starts the stopwatch the exact moment they see the blocks hit, and stops the stopwatch the moment they hear the echo return from the wall. The speed is then calculated using distance divided by time. To reduce errors caused by human reaction time, the person clapping can synchronize their claps with the returning echoes over a set of 20 intervals, and the total time can be measured.

Worked Example: Echo Calculation

Two students stand $80\text{ m}$ from a large brick building. One student hits two blocks together, and the other measures a time of $0.48\text{ s}$ between seeing the impact and hearing the echo. Calculate the speed of sound in air.

Step 1: Calculate the total distance the sound wave travelled.

• The sound must travel to the wall AND back to the students.
• $\text{Total distance} = 80\text{ m} \times 2 = 160\text{ m}$

Step 2: State the formula for speed.

Step 3: Substitute the values and calculate.

• $v = \frac{160\text{ m}}{0.48\text{ s}}$
• $v = 333.3\text{ m/s}$