One end of a string is attached to a vibrator. The string is stretched by passing the other end over a pulley and attaching a load, as illustrated in Fig. 4.1.

Question 5

(a) State the conditions required for the formation of stationary waves. [2]

(b) One end of a string is attached to a vibrator. The string is stretched by passing the other end over a pulley and attaching a load, as illustrated in Fig. 4.1.

Fig. 4.1

The frequency of vibration of the vibrator is adjusted to 250 Hz and a transverse wave travels along the string with a speed of 12 m s^-1. The wave is reflected at the pulley and a stationary wave forms on the string.

Fig. 4.2 shows the string between points A and B at time t = t1.

Fig. 4.2

At time t = t₁ the string has maximum displacement.

(i) Calculate the distance AB. [2]

(ii) On Fig. 4.2, sketch the position of the string between A and B at times

1. t = t₁ + 2.0 ms (label this line P),

2. t = t₁ + 5.0 ms (label this line Q).

[3]

[Total: 7]

Reference: Past Exam Paper – June 2017 Paper 21 Q4

Solution:

(a)

Stationary waves are formed when two waves of the same type and having the same frequency and speed overlap.as they travel in opposite directions.

(b)

(i)

{AB corresponds to 1.5 waves.

From the equation v = fλ,}

λ = 12 / 250 (= 0.048 m)

distance AB = 1.5 × 0.048 = 0.072 m

(ii)

Period T (= 1/f) = 1 / 250 = 0.004 (s) or 4 (ms)

{The wave takes 4.0 ms to return to this position again.

After 1.0 ms, the wave is horizontal

After 2.0 ms, the wave is as shown by P.

After 3.0 ms, the wave is horizontal again.

After 4.0 ms, the wave returns to its original position shown in the question.

The above 4 steps repeats over and over.

After 5.0 ms, the wave is horizontal.}

1. curve drawn is mirror image of that in Fig. 4.2 and labelled P

2. horizontal line drawn between A and B and labelled Q