Two speakers, one at the origin and the other facing it at x = 1.04 m, are driven by the same oscillator at a frequency of 642 Hz. If the speed of sound is 343 m/s, find the following.

I know the wavelength is .53 m how do I do b?

(b) the location of a point of destructive interference closest to 0.520 m on the interval [0, 0.520 m]

To find the location of a point of destructive interference closest to 0.520 m, we need to determine the path difference between the two speakers at that point.

First, let's calculate the distance traveled by the sound wave from the first speaker to the point of interest (0.520 m). Given that the first speaker is at the origin, the distance is simply 0.520 m.

Next, let's calculate the distance traveled by the sound wave from the second speaker to the point of interest. The second speaker is located at x = 1.04 m. So, the distance from the second speaker to the point of interest is (1.04 m - 0.520 m) = 0.520 m.

Now, let's find the path difference by taking the absolute value of the difference between the two distances:

Path difference = |distance from first speaker - distance from second speaker|
= |0.520 m - 0.520 m|
= 0 m

Since destructive interference occurs when the path difference is an integer multiple of the wavelength, and the path difference is 0, we can conclude that the point at 0.520 m experiences destructive interference.

Therefore, the location of a point of destructive interference closest to 0.520 m is exactly at 0.520 m.