If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:

1.  \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\)
2. \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\)
3. \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\)
4. \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\)

Subtopic:  Wave Motion |
 85%
From NCERT
AIPMT - 2002
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The phase difference between two waves, represented by
y1=106sin{100t+(x/50)+0.5}my2=106cos{100t+(x50)}m
where X is expressed in metres and t is expressed in seconds, is approximate:
1. 2.07 radians
2. 0.5 radians
3. 1.5 radians
4. 1.07 radians

Subtopic:  Wave Motion |
 59%
From NCERT
AIPMT - 2004
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A point source emits sound equally in all directions in a non-absorbing medium. Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)

Subtopic:  Energy of Waves |
 73%
From NCERT
AIPMT - 2005
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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 percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be:

1. 1%

2. 2%

3. 3%

4. 4%

Subtopic:  Travelling Wave on String |
 86%
From NCERT
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The equation of a wave on a string of linear mass density \(0.04 \mathrm{~kg} \mathrm{~m}^{-1}\) is given by: 
\({y}{=}{0}{.}{02}\left({m}\right)\sin\left[{{2}\mathit{\pi}\left({\frac{t}{{0}{.}{04}\left({s}\right)}{-}\frac{x}{{0}{.}{50}\left({m}\right)}}\right)}\right]\). The tension in the string will be:
1. \(4.0~\text{N}\) 2. \(12.5~\text{N}\)
3. \(0.5~\text{N}\) 4. \(6.25~\text{N}\)
Subtopic:  Travelling Wave on String |
 76%
From NCERT
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A one-meter long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the minimum tube length is 25.5 cm. The speed of sound in air at the temperature of the experiment is: (The edge effects may be neglected.)

1. 324.16 m/s

2. 320 m/s

3. 345 m/s

4. 346.8 m/s

Subtopic:  Standing Waves |
 67%
From NCERT
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A bat emits an ultrasonic sound of frequency \(1000\) kHz in the air. If the sound meets a water surface, what is the wavelength of the reflected sound? (The speed of sound in air is \(340\) m/sec and in water is \(1486\) m/sec)
1. \(3.4 \times 10^{-4}~\text{m}\)
2. \(1 . 49 \times 10^{- 3}  ~ \text{m}\)
3. \(2 . 34 \times 10^{- 2}   ~\text{m}\)
4. \(1 . 73 \times10^{- 3}   ~\text{m}\)

Subtopic:  Speed of Sound |
 55%
From NCERT
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A steel wire has a length of \(12.0\) m and a mass of \(2.10\) kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at \(20^{\circ}\mathrm{C}\) (which is \(343\) m/s)?
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N

Subtopic:  Travelling Wave on String |
 74%
From NCERT
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A person standing between two parallel hills fires a gun and hears the first echo after t1 sec and the second echo after t2 sec. The distance between the two hills is: [Given: Speed of sound = v]

1. vt1-t22
2. vt1t22t1+t2
3. vt1+t2
4. vt1+t22

Subtopic:  Speed of Sound |
 55%
From NCERT
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