__Question 1__

A uniform string is held between a fixed point P and a
variable-frequency oscillator, as shown in Fig. 5.1.

**Fig. 5.1**

The distance between point P and the oscillator is *L*.

The frequency of the oscillator is adjusted so that the
stationary wave shown in Fig. 5.1 is formed.

Points X and Y are two points on the string.

Point X is a distance 1/8 L from the end of the string
attached to the oscillator. It vibrates with frequency *f *and amplitude *A*.

Point Y is a distance 1/8 L from the end P of the string.

**(a) **For the vibrations of point Y, state

**(i) **the frequency (in terms of *f *), [1]

**(ii) **the amplitude (in terms of *A*).
[1]

**(b) **State the phase difference between the vibrations of
point X and point Y. [1]

**(c) (i) **State, in terms of *f *and *L*,
the speed of the wave on the string. [1]

**(ii) **The wave on the string is a stationary
wave.

Explain, by reference to the formation of a stationary
wave, what is meant by the

speed stated in **(i)**. [3]

**Reference:** *Past Exam Paper – November 2009 Paper 22 Q5*

**Solution 1:**

**(a) **

**(i) **f **[B1]**

**(ii) **A **[B1]**

{Amplitude
means maximum displacement.}

**(b) **180^{o} or π rad (unit necessary) **[B1]**

{When talking about the phase of a point, we need to
consider its displacement and the direction of motion/vibration.

Phase difference between 2 points means the difference in
phase about the 2 points.

Point X and Y are at the same displacement (one is +ve
and the other -ve). However, they moving in opposite direction. So, they are
out of phase (phase difference = 180°).}

**(c) (i) **Speed
of wave = f x L **[B1]**

**(ii) **

The wave is reflected at the end /
at P. **[B1]**

EITHER The incident and reflected
waves interfere OR the two waves travelling in opposite directions interfere. **[M1]**

The speed is the speed of incident
or reflected wave / one of these waves. **[A1]**