Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 19 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 52 cm .
Required:
Part A) What is the wavelength of the sound?Part B) If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?

Answer 1

Answer:

The wave length of the sound is 66 cm.

The separation between the speakers is 85 cm.

Explanation:

Given that,

Distance between the speakers = 19 cm

Reaching zero at separation  = 52 cm

(a). We need to calculate the wave length of the sound

Using formula of wavelength

$\dfrac{\lambda}{2}=\Delta x_{2}-\Delta x_{1}$

$\lambda=2\times(\Delta x_{2}-\Delta x_{1})$

Put the value into the formula

$\lambda=2\times(52-19)$

$\lambda=66\ cm$

The wave length of the sound is 66 cm.

(b). if the distance between the speakers continues to increase the intensity will again be a maximum when the separation between the speakers that produces a maximum has increased by one wave length

We need to calculate the separation between the speakers

Using formula of separation

$d=19+66$

$d=85\ cm$

The separation between the speakers is 85 cm.

Hence, The wave length of the sound is 66 cm.

The separation between the speakers is 85 cm.