A student investigates transverse waves on a long string held under constant tension. Using a high-speed camera, the student measures the wavelength corresponding to several driver frequencies. The results are recorded below (measurement uncertainties are ignored unless specified).
Frequency (Hz) | Measured Wavelength (m)
10 | 0.64
15 | 0.43
20 | 0.32
25 | 0.26
(1) For each pair of data in the table, calculate the wave speed. Add a clearly labelled column of speeds to the table.
(2) Use your results from part (a) to evaluate whether the wave speed can be considered constant over the frequency range tested. Support your conclusion with quantitative evidence.
(3) The camera has an uncertainty of ±0.01 m in measuring wavelength, and the function generator has an uncertainty of ±0.1 Hz in frequency. For the 20 Hz data point, compute the percent uncertainty in the calculated wave speed. Show all work.
(4) Suppose the student wishes to halve the wavelength relative to the 25 Hz data point while keeping the wave speed unchanged. Determine the driver frequency that should be selected and explain your reasoning.