Question

You are 2m from one audio speaker and 2.1m from another audio speaker. Both generate the identical sine wave with a frequency of 680 Hz. At your location, what is the phase difference between the waves? Give the answer in radians, using 340m/s as the velocity of sound.

Answer 1

Answer:

the phase difference is 1.26 radian

Solution:

As per the question:

Distance, d = 2 m

Distance from the other speaker, d' = 2.1 m

Frequency, f = 680 Hz

Speed of sound, v = 340 m/s

Now,

To calculate the phase difference, $\Delta \phi$:

Path difference, $\Delta d = d' - d = 2.1 - 2 = 0.1\ m$

For the wavelength:

$f\lambda = v$

where

c = speed of light in vacuum

$\lambda$ = wavelength

Now,

$680\times \lambda = 340$

$\lambda = 0.5\ m$

Now,

Phase difference, $\Delta phi = 2\pi \frac{\Delta d}{\lambda}$

$\Delta phi = 2\pi \frac{0.1}{0.5} = 1.26\ rad$