RP8: Wave Measurements in Liquids and Solids

Wavelength is the distance along the direction of travel for one full cycle, such as crest to the next crest. Frequency counts cycles passing a point per second; period is the time for one cycle. Measure several complete spacings or cycles and divide by the number of intervals to reduce the fractional effect of a single reading uncertainty. Six crest marks define five adjacent crest-to-crest intervals, not six.

For one wave in a consistent medium, v = fλ. A distance divided by the time taken by a recognisable wave disturbance provides another speed estimate. Do not multiply frequency from one setting by wavelength from another. Changing water depth can change wave speed, so record depth and keep the relevant conditions comparable when testing relationships.

A ripple tank makes water-wave patterns visible, often by projecting shadows onto a screen. Measure the pattern scale against a known distance in the same projection arrangement: a magnified shadow is not automatically the actual wavelength. A still image or suitable synchronised strobe can help identify crests, but a visually stationary pattern does not mean the water-wave frequency is zero.

Use a suitable low-amplitude wave pattern and identify a region where the crests are clear. Count cycles over an appropriately long timed interval or use a correctly interpreted drive-frequency reading. Keep the tank level and minimise unwanted reflections where appropriate. Explain why the selected apparatus can resolve the frequency and distances being measured; merely naming a stopwatch is insufficient for a rapidly vibrating system.

A wave in a stretched string can be driven by a signal generator, with its frequency read from the source and its wavelength inferred from a clear pattern. For a standing wave, neighbouring nodes are separated by half a wavelength, so the whole visible length is not automatically one wavelength. State the boundary conditions and the number of loops before using the length.

A longitudinal vibration in a suitable metal rod is a different solid-wave method. In an appropriate fundamental longitudinal mode with a central node and free ends, rod length corresponds to half a wavelength, so λ = 2L. A microphone and suitable frequency display can identify a resonance, but selecting a harmonic instead of the fundamental changes the interpretation. Use the centre’s approved support/excitation arrangement. Pearson explicitly requires the metal-rod context; a string demonstration alone does not fulfil that named subpart.

Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.