In a guitar, two strings \(A\) and \(B\) made of same material are slightly out of tune and produce beats of frequency \(6~\text{Hz}\). When tension in \(B\) is slightly decreased, the beat frequency increases to \(7~\text{Hz}\).  If the frequency of \(A\) is \(530~\text{Hz}\), the original frequency of \(B\) will be:

1. \(524~\text{Hz}\) 2. \(536~\text{Hz}\)
3. \(537~\text{Hz}\) 4. \(523~\text{Hz}\)

Subtopic:  Beats |
 66%
From NCERT
NEET - 2020
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The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz? 

1. \(75\) cm 2. \(60\) cm
3. \(45\) cm 4. \(80\) cm
Subtopic:  Standing Waves |
 82%
From NCERT
NEET - 2020
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A tuning fork with a frequency of \(800\) Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of \(9.75\) cm, \(31.25\) cm, and \(52.75\) cm. The speed of the sound in the air is:

1. \(500\) m/s 2. \(156\) m/s
3. \(344\) m/s 4. \(172\) m/s
Subtopic:  Speed of Sound |
 74%
From NCERT
NEET - 2019
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The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:
1. \(\frac{3\pi}{2}\)
2. \(3\pi\)
3. \(\frac{2\pi}{3}\)
4. \(2\pi\)

Subtopic:  Wave Motion |
 74%
From NCERT
AIPMT - 2012
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Two identical piano wires, kept under the same tension T, have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be:

1. 0.01

2. 0.02

3. 0.03

4. 0.04

Subtopic:  Beats |
 62%
From NCERT
AIPMT - 2011
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For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

Subtopic:  Wave Motion |
 73%
From NCERT
AIPMT - 1998
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Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:

1. 2uλ

2. uλ

3. μλ

4. μ2λ

Subtopic:  Beats |
 58%
From NCERT
AIPMT - 2000
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A string is cut into three parts, having fundamental frequencies n1, n2, and nrespectively. The original fundamental frequency "n" is related by the expression:

1. 1n=1n1+1n2+1n3

2. n=n1×n2×n3

3. n=n1+n2+n3

4. n=n1+n2+n33

Subtopic:  Standing Waves |
 84%
From NCERT
AIPMT - 2000
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The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + α), where δ = α + π/2, then the resultant wave can be represented by:

1. a circle (c.w)

2. a circle (a.c.w)

3. an ellipse (c.w)

4. an ellipse (a.c.w)

Subtopic:  Standing Waves |
 52%
From NCERT
AIPMT - 2000
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Two vibrating tuning forks produce progressive waves given by \(Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}\) and \(Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}\). The number of beats produced per minute is:

1. \(3\) 2. \(360\)
3. \(180\) 4. \(60\)
Subtopic:  Beats |
 57%
From NCERT
AIPMT - 2005
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