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Q. No.The equation of vibration of a taut string, fixed at both ends, is given by: \(y=(4~\text{mm})~\cos\left(\dfrac{\pi x}{30~\text{cm}}\right)~\sin\Big(400\pi s^{-1}t\Big) \)
At which points is the amplitude equal to \(2\) mm?
At which points is the amplitude equal to \(2\) mm?
| 1. | \(x = \) \(10\) cm, \(20\) cm, \(30\) cm, \(40\) cm |
| 2. | \(x=\) \(10\) cm, \(15\) cm, \(30\) cm, \(45\) cm |
| 3. | \(x =\) \(10\) cm, \(20\) cm, \(40\) cm, \(80\) cm |
| 4. | \(x = \) \(10\) cm, \(20\) cm, \(40\) cm, \(50\) cm |
Subtopic: Standing Waves |
From NCERT
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Increasing the wave amplitude of a standing wave will:
| 1. | increase the number of nodes. |
| 2. | increase the number of antinodes. |
| 3. | increase the displacement of the cord at a node. |
| 4. | increase the displacement of the cord at an antinode. |
Subtopic: Standing Waves |
58%
From NCERT
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Suppose a string is \(20\) m long. Which of the following wavelengths is possible for standing waves on this string?
| 1. | \(3.5\) m | 2. | \(13.3\) m |
| 3. | \(30\) m | 4. | \(80\) m |
Subtopic: Standing Waves |
From NCERT
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A taut string of length \(2\) m is fixed at both ends and plucked. The speed of waves on the string is \(3\times10^4\) m/s (see figure).
If the wavelength of the fundamental frequency is \(\lambda_1,\) and the wavelength of the second harmonic is \(\lambda_2,\) what is the ratio \(\dfrac{\lambda_1}{\lambda_2}?\)
| 1. | \(0.5\) | 2. | \(1\) |
| 3. | \(2\) | 4. | \(4\) |
Subtopic: Standing Waves |
54%
From NCERT
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A wire of length \(2L\) is formed by joining two wires, \(A\) and \(B,\) each of the same length but with different radii, \(r\) and \(2r,\) respectively, and made of the same material. The wire vibrates at a frequency such that the joint between the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and in wire \(B\) is \(q,\) the ratio \(p:q\) is:
| 1. | \(3:5\) | 2. | \(4:9\) |
| 3. | \(1:2\) | 4. | \(1:4\) |
Subtopic: Standing Waves |
60%
From NCERT
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