Essay Question :
1 a) State two necessary conditions for the formation of standing waves.
b) A standing wave on a stretched string is represented by
y = 3.0 cos (0.10x) sin (85t), where y and x are in centimetres, and
t is in seconds.
i) Determine the distance between two consecutive nodes.
ii) Calculate the velocity of the waves which formed the standing wave.
c) A long tube which has a tap fitted to it, and filled with water is shown in
the diagram below.
A tuning fork, of frequency 512 Hz, is sounded above the tube as the
water flows out slowly through the tap. The first loud sound is heard
when the length of the air column is 15.7 cm. As the water continues to
flow out, a second loud sound is heard when the length of the air
column is 48.1 cm.
i) Sketch the stationary waves in the tube when the loud sounds are
heard.
ii) What is meant by an end-correction?
iii) Determine the velocity of sound and the end-correction for the tube.

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