In a ripple tank demonstration, two point sources of water waves, P and Q, vibrate in phase at a frequency of 10Hz. The waves travel at 0.30ms−1 across the water’s surface. Consider a point R in the tank where the difference in distances traveled by the waves from P and Q is measured to be 0.75 times the wavelength.
(a) Calculate the wavelength of the water waves.
(b) Using the given path-length difference, classify the interference observed at point R as constructive, destructive, or intermediate. Justify your answer without quoting memorized formulas.
(c) The instructor wants to adjust only the phase of source Q (keeping its frequency and amplitude unchanged) so that point R becomes a position of complete constructive interference. Determine the smallest additional phase shift, expressed both in radians and as a fraction of 2π, that must be applied to source Q.
(d) Describe qualitatively how the overall interference pattern in the tank would change if the frequency of both sources were doubled while their phase relation and positions remained the same.