The equation of a stationary wave is \(y = 0.8 ~cos\left(\frac{\pi x}{20}\right)sin200(\pi t)\), where \(x\) is in cm and \(t\) is in sec. The separation between consecutive nodes will be:

1. \(20~\text{cm}\)

2. \(10~\text{cm}\)

3. \(40~\text{cm}\)

4. \(30~\text{cm}\)

Subtopic:  Standing Waves |
 77%
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A wave represented by the given equation y=acos(kxωt) is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

(1) y=asin(kx+ωt)

(2) y=acos(kx+ωt)

(3) y=acos(kxωt)

(4) y=asin(kxωt)

Subtopic:  Standing Waves |
 55%
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A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :

1. 1.21 Å

2. 2.42 Å

3. 6.05 Å

4. 3.63 Å

Subtopic:  Standing Waves |
 79%
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In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :

(1) Zero

(2) π/2

(3) π

(4) 3π/2

Subtopic:  Standing Waves |
 81%
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A standing wave is represented by

Y=Asin(100t)cos(0.01x)

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

(1) 104 m/s

(2) 1 m/s

(3) 10–4 m/s

(4) Not derivable from the above data

Subtopic:  Standing Waves |
 84%
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Two waves are approaching each other with a velocity of 20 m/s and frequency n. The distance between two consecutive nodes is :

(1) 20n

(2) 10n

(3) 5n

(4) n10

Subtopic:  Standing Waves |
 77%
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The following equations represent progressive transverse waves Z1=Acos(ωtkx), Z2=Acos(ωt+kx), Z3=Acos(ωt+ky) and Z4=Acos(2ωt2ky). A stationary wave will be formed by superposing :

(1) Z1 and Z2

(2) Z1 and Z4

(3) Z2 and Z3

(4) Z3 and Z4

Subtopic:  Standing Waves |
 82%
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Two traveling waves y1=Asin[k(xct)] and y2=Asin[k(x+ct)] are superimposed on the string. The distance between adjacent nodes is :

(1) ct / π

(2) ct / 2π

(3) π / 2k

(4) π / k

Subtopic:  Standing Waves |
 75%
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A string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is :

(1) l4

(2) l2

(3) l

(4) 2l

Subtopic:  Travelling Wave on String |
 64%
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A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to 14cm  keeping the tension unaltered, the new fundamental frequency will be :

(1) 64

(2) 256

(3) 512

(4) 1024

Subtopic:  Travelling Wave on String |
 70%
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