Question

Two loudspeakers in a 20°C room emit 686 Hz sound waves along the x-axis. What is the smallest distance between the speakers for which the interference of the sound waves is destructive?

Answer 1

0.25 m

Step-by-step explanation:

v = Speed of sound in air at 20°C = 343 m/s

f = Frequency = 686 Hz

Wavelength is given by

`\lambda=(v)/(f)\\\Rightarrow \lambda=(343)/(686)\\\Rightarrow \lambda=0.5\ m`

The wavelength is 0.5 m

Path difference for destructive interference

`\Delta x=(\lambda)/(2)\\\Rightarrow \Delta x=(0.5)/(2)\\\Rightarrow \Delta x=0.25\ m`

The required distance is 0.25 m