An observer is located directly between two speakers, located 20m apart. The speakers are in phase with each other, and both are emitting a sound with a frequency of 60Hz. How far away from the centre should the observer move to get the first destructive interference?
you want them to be 1/2 wavelength off.
on path length. ..
To find the distance from the center where the observer experiences the first destructive interference, we can use the concept of wavelength and phase difference between the speakers.
First, we need to find the wavelength of the sound wave being emitted by the speakers. The formula to calculate the wavelength is:
wavelength = speed of sound / frequency
The speed of sound in air is approximately 343 meters per second. So, for a frequency of 60Hz, the wavelength can be calculated as:
wavelength = 343 m/s / 60 Hz
wavelength ≈ 5.72 meters
Since the speakers are emitting waves in phase with each other, the areas where the waves from both speakers meet in phase are called constructive interference regions, and those where the waves meet out of phase are called destructive interference regions.
In the case of destructive interference, the waves from each speaker will have a phase difference of 180 degrees or half a wavelength. Therefore, the path difference between the two waves at the observer's location in the destructive interference region will be equal to an odd multiple of half a wavelength.
So, let's consider the observer starting at the center (the mid-point between the speakers) and moving away to the right. The paths taken by the sound waves from both speakers to reach the observer will have a difference in distance. To calculate this path difference required to produce destructive interference, we can use the following formula:
path difference = n * wavelength / 2
where n is an odd integer (1, 3, 5, ...).
For the first destructive interference, n would be 1.
path difference = (1 * 5.72m) / 2
path difference = 2.86 meters
Hence, the observer needs to move 2.86 meters away from the center towards the right to experience the first destructive interference.