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:
- $10$ 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?
- A band playing music at a frequency f is moving towards a wall at a speed $v_b$. A motorist is following the band with a speed $v_m$. If v be the speed of the sound, the expression for beat frequency heard by motorist is
Questions Asked in NEET exam
- Given below are two statements :
Statement I : In the nephron, the descending limb of loop of Henle is impermeable to water and permeable to electrolytes.
Statement II : The proximal convoluted tubule is lined by simple columnar brush border epithelium and increases the surface area for reabsorption.
In the light of the above statements, choose the correct answer from the option given below :- NEET (UG) - 2024
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The potential (V) at any axial point, at 2 m distance(r) from the centre of the dipole of dipole moment vector\(\vec{P}\) of magnitude, 4 × 10-6 C m, is ± 9 × 103 V.
(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)
Reason R : \(V=±\frac{2P}{4\pi \epsilon_0r^2}\), where r is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below :- NEET (UG) - 2024
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- \(^{290}_{82}X\stackrel{\alpha}{\rightarrow}Y\stackrel{e^+}{\rightarrow}Z\stackrel{\beta^-}{\rightarrow}P\stackrel{e^-}{\rightarrow}Q\)
In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are :- NEET (UG) - 2024
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The output (Y) of the given logic gate is similar to the output of an/a :
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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.