A standing sound wave is set up between a loudspeaker and a wall.

Question 14

A standing sound wave is set up between a loudspeaker and a wall.

A microphone is connected to a cathode-ray oscilloscope (c.r.o.) and is moved along a line directly between the loudspeaker and the wall. The amplitude of the trace on the c.r.o. rises to a maximum at a position X, falls to a minimum and then rises once again to a maximum at a position Y.

The distance between X and Y is 33 cm. The speed of sound in air is 330 m s^-1.

Which diagram represents the c.r.o. trace of the sound received at X?

Reference: Past Exam Paper – June 2012 Paper 12 Q30

Solution:

Answer: B.

In a stationary wave, we have nodes (points with zero amplitude) and antinodes (positions with maximum amplitude).

The maximum at X and Y correspond to antinodes.

Distance between 2 antinodes = λ / 2 = 0.33 m

Wavelength λ = 2 × 0.33 = 0.66 m

v = f λ = λ / T

Period T = λ / v = 0.66 / 330 = 0.002 s = 2.0×10^-3 s

The time-base setting is 0.50 ms / cm.

0.50×10^-3 s - - - > 1 cm (1 square)

Period (= 0.002 s) - - - > [1/(0.50×10^-3)] × 2.0×10^-3 = 4 cm (4 squares)

 
So, one complete wave should take up 4 cm (4 squares).