Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 15 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 65 cm .

Required:
What is the wavelength of the sound?

Answer 1

100 cm

Step-by-step explanation:

It is given that there are two loudspeakers that produces
`$\text{sound waves }$` along x-axis.

The maximum intensity of the sound is
`$\text{when the speakers are}$` at a distance of = 15 cm apart.

The sound intensity becomes zero when the separation between the speakers are increased and becomes 65 cm.

Therefore, the sound waves are in the phase,
`$\Delta x_1=15 \ cm$`

The sound waves are out of phase when
`$\Delta x_2=65 \ cm$`

Therefore,

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

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

= 2 (65 - 15)

= 2 x 50

= 100 cm

Hence the wavelength of the sound is 100 cm.