9702/Oct Nov/12/2016/Q24

A transverse progressive wave of wavelength λ is set up on a stretched string. The graph shows
the variation of displacement y with distance x at a particular instant of time. The displacement
where distance x = λ/8 is y₁.

What are the next two values of x where the displacement y is again equal to y₁?

Solution:

Answer: B

From the figure above, it is very obvious the option C and D are incorrect.

The answer is "B" is because the second value of x must more than λ.

Reference: PYQ - Oct/Nov 2016 Paper 12 Q24

9702/May Jun/12/2015/Q24

Two light waves of the same frequency are represented by the diagram.

What could be the phase difference between the two waves?

A 150°
B 220°
C 260°
D 330°

Solution:

Answer: C

The 2 light waves are said to have the same frequency. The waves have a sinusoidal form.

Let the wave with the larger amplitude be wave A and the one with smaller amplitude be wave B.

Since both waves have a sinusoidal form, we can assume that any of the 2 waves will start at displacement = 0 (we take this point as the reference point), and then move up – just like the wave A at (0, 0).

{In fact, any point (at any displacement) could be taken as the reference point, but in this question, it is easier to consider that point.}

On the graph, the x-axis gives the phase angle.

At a phase of 0°, wave B has not yet reaching the starting (reference) point while wave A is already at that point. It is only at a phase of 100° that wave B reached the reference point (or we could say that wave B reaches this point AGAIN at 100°).

The solution of 100° is not available in the 4 choices, so we can say that wave B had actually already reached this point before – we need to find at which phase this was, according to the x-axis in the diagram.

The phase angle is actually between 0° and 359°. A phase difference of 360° is the same as a phase difference of 0° and a phase difference of 1° is the same as a phase difference of 361°, ….

The wavelength of a wave corresponds to a phase difference of 360°. Since the 2 light waves have the same frequency, it means that they are the same wavelength.

So, if wave B reached the reference point again at a phase of 100°, according to the x-axis, going back by a wavelength (by a phase difference of 360°), we can say that previously, wave B had reached the reference point at the phase of

Phase = 100 – 360 = – 260°

As for wave A, it reaches the reference point at a phase of 0° (according to the x-axis).

Thus, phase difference between wave A and B = 0 – (–260) = 260°

Reference: PYQ - May/Jun 2015 Paper 12 Q24

9702/Oct Nov/11/2016/Q24

The diagram shows an experiment to produce a stationary wave in an air column. A tuning fork,

placed above the column, vibrates and produces a sound wave. The length of the air column can

be varied by altering the volume of the water in the tube.

The tube is filled and then water is allowed to run out of it. The first two stationary waves occur

when the air column lengths are 0.14 m and 0.42 m.

What is the wavelength of the sound wave?

A 0.14 m 

B 0.28 m 

C 0.42 m 

D 0.56 m

Solution:
Answer: D

From the figure of first two stationary waves occur when the air column lengths are 0.14m and 0.42m, we can conclude that

½ wavelength = 0.42 – 0.14

    wavelength = 2 (0.28)

                        = 0.56 m

Reference: PYQ - Oct/Nov 2016 Paper 11 Q24