Two loudspeakers emit sound waves along the x-axis. The

sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm.

a. What is the wavelength of the sound?

b. If the distance between the speakers continues to increase, at

what separation will the sound intensity again be a maximum?

For maximum intensity, distance between speakers is$∆x_1=20cm$

For zero intensity, distance between speakers is$∆x_2=60cm$

We know that the interference of waves occurs due to the phase difference between two waves.

Therefore, according to the condition of interference, if $\lambda$is the wavelength of the sound wave, then we can write,

$$\begin{gathered} ∆x_2-∆x_1=\frac{\lambda }{2} \\ \left(60-20\right)cm=\frac{\lambda }{2} \\ \lambda =\left(2\times 40\right)cm \\ \lambda =80cm \end{gathered}$$

For interference of waves, the distance between two maxima or minima is equal to the wavelength of the sound wave.

Initially, the difference between two speakers for maximum intensity was $∆x_1=20cm$

Wavelength of the sound wave is $\lambda =80cm$

Therefore, if the distance between the speakers is increased, the distance between the speakers should be, role="math" localid="1650036999665" $\left(20+80\right)cm=100cm$when the speakers will be at maximum intensity again.