Question

Two loudspeakers emit identical sound waves along the x-axis. The sound at a point on the axis 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 30 cm.(a) What is the wavelength of the sound

Answer 1

The concept required to solve this problem is related to the wavelength.

The wavelength can be defined as the distance between two positive crests of a wave.

The waves are in phase, then the first distance is

$\Delta x_1 = 20cm$

And out of the phase when

$\Delta x_2 = 30cm$

Thus the wavelength is

$\Delta x_2-\Delta x_1 = \frac{\lambda}{2}$

Here,

$\lambda =$  Wavelength

If we rearrange the equation to find it, we will have

$\lambda = 2 (\Delta x_2-\Delta x_1 )$

$\lambda= 2(30-20)$

$\lambda = 20cm$

Therefore the wavelength of the sound is 20cm.