Q. No.The equation of a plane progressive wave is given by \(y=5 \cos \pi\left(200 t-\dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is: (in m/s)
1. \(120\)
2. \(150\)
3. \(200\)
4. \(300\)
1. \(120\)
2. \(150\)
3. \(200\)
4. \(300\)
Subtopic: Travelling Wave on String |
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Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section \(R \) is \(v_1\) and that in the other string having radius of cross section \(\dfrac{R}{2} \) is \(v_2.\) Then \(\dfrac{v_2}{v_1} =\)
1. \(\sqrt{2} \)
2. \(2\)
3. \(8\)
4. \(4\)
1. \(\sqrt{2} \)
2. \(2\)
3. \(8\)
4. \(4\)
Subtopic: Travelling Wave on String |
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The equation of a wave travelling on a string is \(y = \sin[20πx+10πt], \) where \(x \) and \(t \) are distance and time in \(\text{SI}\) units. The minimum distance between two points having the same oscillating speed is:
1. \(2.5~\text{cm}\)
2. \(20~\text{cm}\)
3. \(10~\text{cm}\)
4. \(5.0~\text{cm}\)
1. \(2.5~\text{cm}\)
2. \(20~\text{cm}\)
3. \(10~\text{cm}\)
4. \(5.0~\text{cm}\)
Subtopic: Travelling Wave on String |
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The equation of a transverse wave travelling along a string is \(y(x,~t)=4.0\sin[20\times 10^{-3}x+600t]~\text{mm},\) where \(x\) is in \(\text{mm}\) and \(t\) is in second. The velocity of the wave is:
1. \(-60~\text{m/s}\)
2. \(+30~\text{m/s}\)
3. \(+60~\text{m/s}\)
4. \(-30~\text{m/s}\)
1. \(-60~\text{m/s}\)
2. \(+30~\text{m/s}\)
3. \(+60~\text{m/s}\)
4. \(-30~\text{m/s}\)
Subtopic: Travelling Wave on String |
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The equation of the progressive wave is given as \(y = 5 ~sin (6t + 0.03 x)\) Find the speed of wave. (Assume all units in SI units)
1. 50 m/s
2. 100 m/s
3. 200 m/s
4. 150 m/s
1. 50 m/s
2. 100 m/s
3. 200 m/s
4. 150 m/s
Subtopic: Travelling Wave on String |
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A string of mass per unit length equal to \(7 \times10^{-3}~\text{kg/m}\) is subjected to a tension equal to \(70~\text{N}\). The speed of the transverse wave on this string is equal to:
1. \(10~\text{m/s}\)
2. \(50~\text{m/s}\)
3. \(100~\text{m/s}\)
4. \(200~\text{m/s}\)
1. \(10~\text{m/s}\)
2. \(50~\text{m/s}\)
3. \(100~\text{m/s}\)
4. \(200~\text{m/s}\)
Subtopic: Travelling Wave on String |
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A transverse wave travels along a uniform wire with a length of \(50\) cm and a mass of \(10~\text{grams}\) at a speed of \(60\) m/s. If the wire has a cross-sectional area of \(2.0\) mm2 and a Young's modulus of \(1.2\times 10^{11}\) N/m2, the extension of the wire over its natural length due to its tension will be:
| 1. | \(0.12\) mm | 2. | \(0.15\) mm |
| 3. | \(0.20\) mm | 4. | \(0.25\) mm |
Subtopic: Travelling Wave on String |
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The mass per unit length of a uniform wire is \(0.135\) g/cm. A transverse wave of the form \(y=-0.21 \sin (x+30 t)\) is produced in it, where \(x\) is in meter and \(t\) is in second. The expected value of the tension in the wire is:
| 1. | \(12.15\) N | 2. | \(30.12\) N |
| 3. | \(45.35\) N | 4. | \(50.24\) N |
Subtopic: Travelling Wave on String |
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The percentage increase in the speed of transverse waves produced in a stretched string when the tension is increased by \(4\%\) is:
1. \(4\%\)
2. \(3\%\)
3. \(2\%\)
4. \(1\%\)
Subtopic: Travelling Wave on String |
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The speed of a transverse wave on a straight wire (mass \(6.0~\text g ,\) length \(60~\text{cm}\) and area of cross-section \(1.0~\text {mm}^2 )\) is \(90~\text {ms}^{-1}.\) If Young's modulus of wire is \(16 \times 10^{11}~\text{Nm}^{-2},\) the extension of wire over its natural length is:
1. \(0.03~\text{mm}\)
2. \(0.01~\text{mm}\)
3. \(0.02~\text{mm}\)
4. \(0.04~\text{mm}\)
1. \(0.03~\text{mm}\)
2. \(0.01~\text{mm}\)
3. \(0.02~\text{mm}\)
4. \(0.04~\text{mm}\)
Subtopic: Travelling Wave on String |
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