Core Practicals 6–7: Sound Speed and Vibrating Strings

Connect a signal generator to a loudspeaker and use a microphone connected to the second oscilloscope channel. Display the source reference signal and received sound simultaneously. Keep frequency fixed, move the microphone along a measured line, and identify positions where the traces have the same phase.

Successive in-phase positions are separated by one wavelength. Measuring across several complete phase cycles reduces fractional position uncertainty. An antiphase position is only half a wavelength from an in-phase position, so compare matching zero-crossing directions or peaks. Calculate c=fλ from the generator frequency and measured spacing.

Drive a string with a vibration generator and signal generator; set tension using a hanging mass over a suitable pulley. Measure the vibrating length between nodes, identify the fundamental or a known harmonic, and determine linear density by weighing a sufficiently long measured sample of string.

For the fundamental, frequency is proportional to 1/L, to √T and to 1/√μ when the other quantities are controlled. Therefore useful graphs include f against 1/L, f² against T and f² against 1/μ. Keep harmonic number fixed and state which variables stay constant.

Find resonance through a clear maximum amplitude rather than the first visible vibration. Repeat tuning from above and below to assess judgement scatter. Small driving amplitudes help avoid changing string tension as the motion grows. Pulley friction means tension may differ slightly from mg.

For sound, reduce confusing room reflections and maintain a consistent microphone alignment. For the string, secure hanging masses and keep clear of the driver. Repeated phase or resonance measurements reduce random uncertainty; they do not correct an incorrectly counted wavelength or harmonic.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.