Tag: beats and its applications

Questions Related to beats and its applications

$y _1 = A cos (2f _1t)$     and $y _2 = A cos (2 f _2t),$, then $y _{total} $ is

physics superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

  1. $y _{total} = y _1 + y _2 = A {cos (2 f _1t) + cos (2 f _2t)}$

  2. $y _{total} = y _1 - y _2 = A {cos (2 f _1t) - cos (2 f _2t)}$

  3. $y _{total} =\dfrac{ y _1}{ y _2} = A\dfrac{{cos (2 f _1t)}}{{cos (2 f _2t)}}$

  4. $y _{total} = y _1 \times y _2 = A {cos (2 f _1t) \times cos (2 f _2t)}$

Show answer
Correct Option: A
Explanation:

Resultant  $(y _{total})$ of the two waves is equal to the superposition of the waves and is given by,
$y _{total}  = y _1+y _2$
$\therefore$  $y _{total} = A \ cos(2f _1t)+ A \ cos(2f _2t)$

A tuning fork of frequency 240 Hz produce 5 beats with a sonometer wire. On increasing the tension in the wire if the number of beats changes to 4 per second, the initial frequency of the wire is

physics superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

  1. 8285 Hz

  2. 275 Hz

  3. 376 Hz

  4. 264 Hz

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Correct Option: A

Two waves of wavelengths 99 cm and 100 cm both travelling with velocity 396 m/s are made of interfere. The number of beats produced by them per second are

physics superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

  1. $1$

  2. $2$

  3. $4$

  4. $8$

Show answer
Correct Option: C
Explanation:

$\begin{array}{l} Velocity\, \, of\, \, wave\, \, V=n\lambda  \ Where\, \, n=frequency\, \, of\, \, wave\, \,  \ \Rightarrow n=\frac { v }{ \lambda  }  \ { n _{ 2 } }=\frac { { { v _{ 2 } } } }{ { { \lambda _{ 2 } } } } =\frac { { 396 } }{ { 100\times { { 10 }^{ -2 } } } } =396Hz \ no.\, \, of\, \, beats\, \, ={ n _{ 1 } }-n _2\, =4 \end{array}$

If 2 waves of same frequency and same amplitude on superposition, produce a resultant disturbance of the same amplitude, the waves differ in phase by

physics superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

  1. $ \dfrac { \pi }{ 3 } $

  2. $ \dfrac { 2\pi }{ 3 } $

  3. $ { \pi } $

  4. $ { 3\pi } $

Show answer
Correct Option: B
Explanation:

Let the amplitude of each wave be $A$ i.e.  $A _1 = A _2 = A$
Thus amplitude of resultant wave  $A _R =A$
Using   $A^2 _R =  A _1^2 + A _2^2 + 2A _1A _2 \cos\theta$
$\therefore$  $A^2 =  A^2 + A^2 + 2A^2 \cos\theta$
Or  $\cos\theta = -0.5$
$\implies  \ \theta = \dfrac{2\pi}{3}$

Two identical wires are stretched by the same tension of $101$ N & each emits a note of frequency $202$ Hz. If the tension in one wire is increased by $1N$ , then the beat frequency is:

physics superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

  1. $2 Hz$

  2. $\frac{1}{2}Hz$

  3. $1 Hz$

  4. None of these

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Correct Option: C