Monday, May 1, 2017

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




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) 180o           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°).}

[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]

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