1.1. Figure 1 shows a vertical cross-section through a water wave moving from left to right.

Figure 1

Deduce the point at which the water is moving upwards at maximum speed and explain your reasoning. 

1.2. While a microphone is connected to an oscilloscope, a student strikes a tuning fork nearby. 

The sound wave produced by the tuning fork is displayed as a trace on the screen. Figure 2 shows the resulting trace.

Figure 2

Use Figure 2 to calculate the wavelength of the sound wave produced. 

(The speed of sound is approximately 330 m s^–1).

1.3. The student’s lab partner strikes another identical tuning fork near the microphone, so that both sound wave signals can be overlaid on the oscilloscope trace. Figure 3 shows the new trace.

Figure 3

Using Figure 3, determine the phase difference between the two signals as shown on the oscilloscope trace. 

Give a suitable unit with your answer.

1.4. The oscilloscope trace is known as a ‘time-view’ of the sound wave because it shows the displacement of an oscillating signal against time. One of the students makes a time-view sketch as shown in Figure 4a, including a label M. 

An oscillating signal can also be shown in terms of a ‘space-view’, which would show the displacement of the signal against its position. The other student makes a space-view sketch as shown in Figure 4b, including a label N.

Figure 4a

Figure 4b

Show that the wave speed v is given by:

                  V=$\frac{3N}{2M}$