Question

two loudspeakers facing each other are separated by 1.00 m and are excited in phase by a 1,100 Hz sine wave. Where will be the points on a line between speakers where there will be constructive interference, and where will be the points where there will be destructive interference

Answer 1

Answer:

Condition of constructive interference is given as

x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm

condition of destructive interference we know that

x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm

Explanation:

As we know that the frequency of the sound waves is 1100 Hz

now we can find the wavelength as

$\lambda = \frac{c}{f}$

now we have

$\lambda = \frac{330}{1100}$

$\lambda = 30 cm$

now we know for the condition of constructive interference

Path difference = N$\lambda$

$(1 - x) - x = N(0.30)$

$1 - 2x = N(0.30)$

$x = \frac{1 - 0.30 N}{2}$

x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm

Similarly for condition of destructive interference we know that

Path difference = (2N + 1)$\frac{\lambda}{2}$

so we have

$(1 - x) - x = (2N + 1)(0.15)$

$1 - 2x = N(0.30) + 0.15$

$x = \frac{0.85 - 0.30 N}{2}$

x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm