Question

A digital delay-device echoes an input signal by repeating it a fixed length of time after it is received. If such a device receives the pure note f₁(t)=5 sin t and echoes the pure note f₂(t)=5 cos t, then the combined sound is f(t)=f₁(t)+f₂(t). Find k and π

Answer 1

To find the combined sound, we add the given wave functions f₁(t) and f₂(t). Comparing the combined sound function to the general form of a wave function, we can find the values of k and π.

Step-by-step explanation:

To find the combined sound, we need to add the two given wave functions: f(t) = f₁(t) + f₂(t). In this case, f₁(t) = 5 sin(t) and f₂(t) = 5 cos(t). Adding these two functions gives us f(t) = 5 sin(t) + 5 cos(t).

To find the values of k and π, we can compare this combined sound function to the general form of a wave function: f(t) = A sin(kx + π), where A is the amplitude and k is the wave number. In our case, we have f(t) = 5 sin(t) + 5 cos(t) = A sin(kx + π).

Comparing the coefficients, we can see that A = 5 and k = 1. Therefore, the values of k and π are 1 and π respectively.