Two sources of sound placed close to each other, are emitting progressive waves given by
$y _{1}=4 \sin 600\, \pi t$ and $y _{2}=5 \sin 608\, \pi t :$ An observer located near these two sources of sound will hear
- 4 beats per second with intensity ratio 25 : 16 between waxing and waning
- 8 beats per second with intensity ratio 25 : 16 between waxing and waning
- 8 beats per second with intensity ratio 81 : 1 between waxing and waning
- 4 beats per second with intensity ratio 81 : 1 between waxing and waning
The Correct Option is D
Solution and Explanation
Comparing with \(y _{1}= a _{1} \sin 2 \pi f _{1} t\)
and \(y _{2}= a _{2} \sin 2 \pi f _{2} t\)
we get \(f_1 =300\, Hz,\, f _{2}=304\, Hz\)
Number of beats \(= f _{2}- f _{1}=4\, s ^{-1}\)
\(\frac{ I _{\max }}{ I _{\min }}=\left(\frac{ a _{1}+ a _{2}}{ a _{1}- a _{2}}\right)^{2}\)
\(=\frac{ I _{\max }}{ I _{\min }}=\left(\frac{4+5}{4-5}\right)^{2}=\frac{81}{1}\)
Top Questions on beats
- The displacement equations of sound waves produced by two sources are given by: \( y_1 = 5 \sin(400t) \) and \( y_2 = 8 \sin(408t) \), where \( t \) is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is:
- If frequencies are \( (v - 1) \) and \( (v + 2) \), then find the value of beats.
- $10$ forks are arranged in increasing order of frequency in such a way that any two nearest tuning forks produce $4$ beats/sec. The highest frequency is twice of the lowest. Possible highest and the lowest frequencies (in $Hz$ ) are
- Two tuning forks A and B produce 4 beats/sec. Forks B and C produce 5 beats/sec. Forks A and C may produce ??. beats/sec
- Two identical piano wires have a fundamental frequency of $600 $ cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of $6$ beats per second when both wires vibrate simultaneously?
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Concepts Used:
Beats
What is Beat Frequency?
Let’s see from fig.m, the frequency of a pink-colored wave is f1, and that of a green-colored wave is f2. So, the frequency of the beat is the difference between these two, which is:
fBEATS = |f1 - f2|
Interference and Beats
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
What is Interference?
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
The Application of Beats:
- Beats are used in determining the unknown frequency
- Beats are used in determining the existence of poisonous gases in mines.