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Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
  1. What are beats? Name the basic phenomenon due to which beats are produced.
  2. Two sources of sound are producing waves of frequency $n_1$ and $n_2$, where $(n_1 - n_2)$ is small, show mathematically that the beat frequency is $(n_1 - n_2)$.
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Answer

  1. Beats: The waxing and waning of sound due to interaction between two slightly different frequencies. If y, and v, are the two frequencies $v_b = |v_1 - v_2|$.
Beats are heard only when $|v_1 - v_2l< 10$, since the sound persist in our ears for $\frac{1}{10}\text{th}$ of a second.
  1. 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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