Question

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?

Short answer

a. The wavelength of the sound is $80cm.$

b. If the distance between the speakers continues to increase, the sound intensity again be a maximum when the separation is$100cm.$

Step-by-step solution

Part a Step 1: Given data

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

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

Determination of wavelength

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,

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

Part b Step 2: Introduction

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

Determination of the separation between the speakers

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.