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Q. No.The equation of a stationary wave is given as \(y =A\sin(0.5\pi t)\cos(0.2\pi x)\) where \(t\) is in seconds and \(x\) in centimetres. Which of the following is correct?
1.
Wavelength of the component waves is \(10~\text{cm}.\)
2.
The separation between a node and the nearest antinode is \(2.5~\text{cm}.\)
3.
Frequency of the component wave is \(0.25~\text{Hz}\).
4.
All of these
Subtopic: Standing Waves |
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The equation of a travelling wave is given as \(y = A\sin(40\pi t-0.2\pi x),\) where \(t\) is in seconds and \(x\) in metres. The minimum distance between two particles oscillating in the same phase is:
1. \(10~\text{m}\)
2. \(5~\text{m}\)
3. \(2~\text{m}\)
4. \(1.5~\text{m}\)
1. \(10~\text{m}\)
2. \(5~\text{m}\)
3. \(2~\text{m}\)
4. \(1.5~\text{m}\)
Subtopic: Wave Motion |
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Two sound waves given by the equations \(y=A\sin 122 \pi t\) and \(y=A\sin 128 \pi t\) pass through a point simultaneously. The number of beats per second is:
| 1. | \(6\) | 2. | \(5\) |
| 3. | \(4\) | 4. | \(3\) |
Subtopic: Beats |
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Stationary waves are formed on a stretched string. If the wavelength is \(\lambda,\) then the distance between two points having the maximum displacement can be:
1. \(\frac{3\lambda}{2}\)
2. \(4\lambda\)
3. \(\frac{5\lambda}{2}\)
4. All of these
1. \(\frac{3\lambda}{2}\)
2. \(4\lambda\)
3. \(\frac{5\lambda}{2}\)
4. All of these
Subtopic: Standing Waves |
66%
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Given the equation for a wave on the string, \(y = 0.5\sin(5x-3t)\) where \(y\) and \(x\) are in metres and \(t\) in seconds, the ratio of the maximum speed of particle to the speed of wave is:
| 1. | \(1:1\) | 2. | \(5:2\) |
| 3. | \(3:2\) | 4. | \(4:5\) |
Subtopic: Wave Motion |
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A car with a siren is moving towards a hill at a speed of 108 km/h. A person is standing at the foot of the hill. The frequency observed by a person is: (frequency of siren is 600 Hz, velocity of sound is 330 m/s)
1. 720 Hz
2. 660 Hz
3. 600 Hz
4. 630 Hz
Subtopic: Doppler's Effect (OLD NCERT) |
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If the transverse displacement of a string clamped at both ends is given by \(y(x,t)= (12~\text{cm}) \sin(6.28x)\cos(3.14t),\) where \(x\) is in cm and \(t\) is in seconds, then which of the following is not true?
| 1. | The velocity of the component wave is \(0.5~\text{cm/s}\). |
| 2. | The amplitude of one of the component waves is \(6~\text{cm}\). |
| 3. | The distance between two consecutive nodes is \(0.5~\text{cm}\). |
| 4. | \(x= 0.25~\text{cm}\) is the first node except the nodes at the ends. |
Subtopic: Standing Waves |
55%
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A string of length \(l\) is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:
1. \(1:2:3:~.......\)
2. \(1:3:5:7~.......\)
3. \(1:2:4:8~.......\)
4. \(1:3:9:~.......\)
1. \(1:2:3:~.......\)
2. \(1:3:5:7~.......\)
3. \(1:2:4:8~.......\)
4. \(1:3:9:~.......\)
Subtopic: Standing Waves |
82%
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A sound wave is passed through a chamber.
If the rms speed of molecules in a gas is \(v_1\) and the speed of sound is \(v_2\) in the gas, then:
1. \(v_1= v_2\)
2. \(v_1> v_2\)
3. \(v_1< v_2\)
4. \(v_1\leq v_2\)
Subtopic: Speed of Sound |
65%
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Stationary waves can be obtained in an air column even if interfering waves have different:
1. Amplitude
2. Wavelength
3. Velocity
4. Frequency
1. Amplitude
2. Wavelength
3. Velocity
4. Frequency
Subtopic: Standing Waves |
58%
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