Question
- What are beats? Name the basic phenomenon due to which beats are produced.
- Two sources of sound are producing waves of frequency n1 and n2, where (n1 - n2) is small, show mathematically that the beat frequency is (n1 - n2).
✓
Answer
- Beats: The waxing and waning of sound due to interaction between two slightly different frequencies. If y, and v, are the two frequencies vb = |v1 - v2|.
Beats are heard only when |v1 - v2l< 10, since the sound persist in our ears for $\frac{1}{10}\text{th}$ of a second.
- When n, and n, are two frequencies represented by $\text{y}_1=\text{A}\sin2\pi\text{n}_1\text{t}$ and $\text{y}_2=\text{A}\sin2\pi\text{n}_2\text{t},$ we get on superposition,
$\text{y}=\text{y}_1+\text{y}_2$
$=2\text{A}\cos\pi\Big(\frac{\text{n}_1-\text{n}_2}{2}\Big)\text{t}\sin2\pi\Big(\frac{\text{n}_1\text{n}_2}+{2}\Big)\text{t}$
Amplitude $=2\text{A}\cos2\pi\Big(\frac{\text{n}_1-\text{n}_2}{2}\Big)\text{t}$ becomes maximum, when $2\pi\text{t}\Big(\frac{\text{n}_1-\text{n}_2}{2}\Big)=0,2\pi...\text{N}\pi\text{ i.e., }\text{n}_1-\text{n}_2=\frac{2\text{N}\pi}{2\pi\text{t}}=\frac{\text{N}}{\text{t}}=\text{N}.$ n where n is the beat frequency-the number of times the maxima and minima is repeated in one second.
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