STILL  MORE  WAVES

1.

A sound source, emitting at 440 Hz, is placed directly above a 2.6 m long tube which stands vertically with the top end (nearest the source) open and the bottom end closed. Water is poured into the tube. For which heights of the water column in the tube will resonance occur?

2.

A uniform steel wire is cut into two pieces of different length; wire #2 is 1${1\over2}$ times as long as wire #1. Each wire piece is fixed at both ends and placed under a tension of 500 N. If the lowest frequency of vibration of wire #1 is 220 Hz, what are the two lowest frequencies at which the two wires will resonate with each other?

3.

A ship is sailing due North at 30 km/hr. Its radio officer is listening to the signals arriving simultaneously from two 90 MHz transmitters broadcasting in phase from positions 1.1 km apart on a North-South line 55 km West of the ship's path. What will be the time interval between detecting successive maxima of the received intensity?

4.

A submarine emits a sound signal at a frequency of 1500 Hz. Maintaining a constant speed of 100 km/hr, it takes evasive action along the path ABCD shown at right. Indicate graphically the wavelength observed at the stationary detector Q as a function of time, specifying precise values. [Note:   $c_{\rm sound} = 1450$ m/s  in water.]