Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 25 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 62 cm .
What is the wavelength of the sound?

Answer 1

Answer:

74 cm

Explanation:

We are given that

The sound has maximum intensity when the separation between speaker=$\Delta x_1=25 cm$

The sound  intensity reaching zero when the separation between speakers=$\Delta x_2=62 cm$

We have to find the wavelength of the sound.

We know that

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

Using the formula

$62-25=\frac{\lambda}{2}$

$37=\frac{\lambda}{2}$

$\lambda=37\times 2=74 cm$

Hence,the wavelength=74 cm

Answer 2

Answer:

λ = 74 cm

Explanation:

given,

Distance at which sound intensity is Maximum = 25 cm

Distance at which sound intensity is zero = 62 cm

When the sound intensity is maximum the condition is constructive interference.

When distance increases the path difference increases.

When means destructive interference the path difference must be increase from nλ to nλ + λ/2

now,

( nλ + λ/2 ) -  n λ = 62 - 25

λ/2 = 37

λ = 37 x 2

λ = 74 cm

Hence, the wavelength of the sound is equal to 74 cm.