__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 Ï€ 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°).}

**[For more explanation on Phase difference, see solution 318 at http://physics-ref.blogspot.com/2015/01/physics-9702-doubts-help-page-55.html]**

**(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]**
Interesting solution :)

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