Speed of a Transverse Wave on a Stretched String
PHXI15:WAVES

354871 A string of length \(l\) hangs from the rigid support \(B\). The linear mass density of the string \(\mu=\mu_{0}\left(\dfrac{x}{l}\right)\). Choose incorrect option from following.
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1 Tension at \(P\) is \(\dfrac{\mu_{0} g x^{2}}{2 l}\)
2 Acceleration of the wave pulse at \(P\) is \(\dfrac{g}{4}\)
3 Time taken by the pulse to move from \(A\) to \(B\) is \(2 \sqrt{\dfrac{l}{g}}\)
4 The distance covered by the wave pulse during the time in which pulse reaches to \(B\) from \(A\) is \(3 l\), if \(B\) is accelerating upwards with \(g\)
PHXI15:WAVES

354872 A block of mass \(M\) hangs from the lowest end of the string of mass \(m\) and length \(l\). A link is generated at \(P\). The time taken by the kink to reach \(Q\) is
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1 \(2 \sqrt{\dfrac{l}{g}}\)
2 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}-\sqrt{M}]\)
3 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M}-\sqrt{m}]\)
4 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}]\)
PHXI15:WAVES

354873 A uniform rope length \(L\) and mass \(m_{1}\) hangs vertically from a rigid support. a block of mass \(m_{2}\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_{1}\) is produced at the lower end of the rope. The wavelength of the pulse when its reaches the top of the rope is \(\lambda_{2}\). the ratio \(\lambda_{2} / \lambda_{1}\) is.

1 \(\sqrt{\dfrac{m_{1}}{m_{2}}}\)
2 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{2}}}\)
3 \(\sqrt{\dfrac{m_{2}}{m_{1}}}\)
4 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{1}}}\)
PHXI15:WAVES

354874 A transverse wave is travelling along a string from left to right. Given figure represents the shape of the string at an instant. Choose the wrong statement for that instant.
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1 Points \({D, E}\) and \({F}\) have positive velocity in upward direction
2 Points \({A, B}\) and \({H}\) have negative velocity in downward direction
3 Points \({C}\) and \({G}\) have zero velocity
4 Points \({A}\) and \({E}\) have minimum velocity
PHXI15:WAVES

354871 A string of length \(l\) hangs from the rigid support \(B\). The linear mass density of the string \(\mu=\mu_{0}\left(\dfrac{x}{l}\right)\). Choose incorrect option from following.
supporting img

1 Tension at \(P\) is \(\dfrac{\mu_{0} g x^{2}}{2 l}\)
2 Acceleration of the wave pulse at \(P\) is \(\dfrac{g}{4}\)
3 Time taken by the pulse to move from \(A\) to \(B\) is \(2 \sqrt{\dfrac{l}{g}}\)
4 The distance covered by the wave pulse during the time in which pulse reaches to \(B\) from \(A\) is \(3 l\), if \(B\) is accelerating upwards with \(g\)
PHXI15:WAVES

354872 A block of mass \(M\) hangs from the lowest end of the string of mass \(m\) and length \(l\). A link is generated at \(P\). The time taken by the kink to reach \(Q\) is
supporting img

1 \(2 \sqrt{\dfrac{l}{g}}\)
2 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}-\sqrt{M}]\)
3 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M}-\sqrt{m}]\)
4 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}]\)
PHXI15:WAVES

354873 A uniform rope length \(L\) and mass \(m_{1}\) hangs vertically from a rigid support. a block of mass \(m_{2}\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_{1}\) is produced at the lower end of the rope. The wavelength of the pulse when its reaches the top of the rope is \(\lambda_{2}\). the ratio \(\lambda_{2} / \lambda_{1}\) is.

1 \(\sqrt{\dfrac{m_{1}}{m_{2}}}\)
2 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{2}}}\)
3 \(\sqrt{\dfrac{m_{2}}{m_{1}}}\)
4 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{1}}}\)
PHXI15:WAVES

354874 A transverse wave is travelling along a string from left to right. Given figure represents the shape of the string at an instant. Choose the wrong statement for that instant.
supporting img

1 Points \({D, E}\) and \({F}\) have positive velocity in upward direction
2 Points \({A, B}\) and \({H}\) have negative velocity in downward direction
3 Points \({C}\) and \({G}\) have zero velocity
4 Points \({A}\) and \({E}\) have minimum velocity
PHXI15:WAVES

354871 A string of length \(l\) hangs from the rigid support \(B\). The linear mass density of the string \(\mu=\mu_{0}\left(\dfrac{x}{l}\right)\). Choose incorrect option from following.
supporting img

1 Tension at \(P\) is \(\dfrac{\mu_{0} g x^{2}}{2 l}\)
2 Acceleration of the wave pulse at \(P\) is \(\dfrac{g}{4}\)
3 Time taken by the pulse to move from \(A\) to \(B\) is \(2 \sqrt{\dfrac{l}{g}}\)
4 The distance covered by the wave pulse during the time in which pulse reaches to \(B\) from \(A\) is \(3 l\), if \(B\) is accelerating upwards with \(g\)
PHXI15:WAVES

354872 A block of mass \(M\) hangs from the lowest end of the string of mass \(m\) and length \(l\). A link is generated at \(P\). The time taken by the kink to reach \(Q\) is
supporting img

1 \(2 \sqrt{\dfrac{l}{g}}\)
2 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}-\sqrt{M}]\)
3 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M}-\sqrt{m}]\)
4 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}]\)
PHXI15:WAVES

354873 A uniform rope length \(L\) and mass \(m_{1}\) hangs vertically from a rigid support. a block of mass \(m_{2}\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_{1}\) is produced at the lower end of the rope. The wavelength of the pulse when its reaches the top of the rope is \(\lambda_{2}\). the ratio \(\lambda_{2} / \lambda_{1}\) is.

1 \(\sqrt{\dfrac{m_{1}}{m_{2}}}\)
2 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{2}}}\)
3 \(\sqrt{\dfrac{m_{2}}{m_{1}}}\)
4 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{1}}}\)
PHXI15:WAVES

354874 A transverse wave is travelling along a string from left to right. Given figure represents the shape of the string at an instant. Choose the wrong statement for that instant.
supporting img

1 Points \({D, E}\) and \({F}\) have positive velocity in upward direction
2 Points \({A, B}\) and \({H}\) have negative velocity in downward direction
3 Points \({C}\) and \({G}\) have zero velocity
4 Points \({A}\) and \({E}\) have minimum velocity
PHXI15:WAVES

354871 A string of length \(l\) hangs from the rigid support \(B\). The linear mass density of the string \(\mu=\mu_{0}\left(\dfrac{x}{l}\right)\). Choose incorrect option from following.
supporting img

1 Tension at \(P\) is \(\dfrac{\mu_{0} g x^{2}}{2 l}\)
2 Acceleration of the wave pulse at \(P\) is \(\dfrac{g}{4}\)
3 Time taken by the pulse to move from \(A\) to \(B\) is \(2 \sqrt{\dfrac{l}{g}}\)
4 The distance covered by the wave pulse during the time in which pulse reaches to \(B\) from \(A\) is \(3 l\), if \(B\) is accelerating upwards with \(g\)
PHXI15:WAVES

354872 A block of mass \(M\) hangs from the lowest end of the string of mass \(m\) and length \(l\). A link is generated at \(P\). The time taken by the kink to reach \(Q\) is
supporting img

1 \(2 \sqrt{\dfrac{l}{g}}\)
2 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}-\sqrt{M}]\)
3 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M}-\sqrt{m}]\)
4 \(2 \sqrt{\dfrac{l}{m g}}[\sqrt{M+m}]\)
PHXI15:WAVES

354873 A uniform rope length \(L\) and mass \(m_{1}\) hangs vertically from a rigid support. a block of mass \(m_{2}\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_{1}\) is produced at the lower end of the rope. The wavelength of the pulse when its reaches the top of the rope is \(\lambda_{2}\). the ratio \(\lambda_{2} / \lambda_{1}\) is.

1 \(\sqrt{\dfrac{m_{1}}{m_{2}}}\)
2 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{2}}}\)
3 \(\sqrt{\dfrac{m_{2}}{m_{1}}}\)
4 \(\sqrt{\dfrac{m_{1}+m_{2}}{m_{1}}}\)
PHXI15:WAVES

354874 A transverse wave is travelling along a string from left to right. Given figure represents the shape of the string at an instant. Choose the wrong statement for that instant.
supporting img

1 Points \({D, E}\) and \({F}\) have positive velocity in upward direction
2 Points \({A, B}\) and \({H}\) have negative velocity in downward direction
3 Points \({C}\) and \({G}\) have zero velocity
4 Points \({A}\) and \({E}\) have minimum velocity