Final answer:
When two close frequencies are played together, they produce beats due to the interference of the sound waves. The equation for beat frequency is fB = |f₁-f₂l. In this case, the two notes are given by f1(t) = cos(11t) and f2(t) = cos(13t). The resulting sound can be graphed by calculating the values of f(t) using the given equations and plotting them on a graph.
Step-by-step explanation:
When two pure notes that are close in frequency are played together, their sounds interfere to produce beats. Beats occur due to the superposition of two waves with slightly different frequencies but the same amplitude. The resulting wave alternates between constructive interference and destructive interference, resulting in a fluctuation in amplitude over time.
The equation for beat frequency is fB = |f₁-f₂l, where f₁ and ₂ are the frequencies of the two original waves. In this case, the two notes are given by f1(t) = cos(11t) and f2(t) = cos(13t). When these two waves are added together, they create the resulting sound f(t) = f1(t) + f2(t).
To graph y = f(t), we can plug in values of t and calculate the corresponding values of f(t) using the given equations. These values can then be plotted on a graph to visualize the waveform.