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

354858 A rope hangs from a rigid support. A pulse is set by jiggling the bottom end. We want to design a rope in which velocity \(v\) of pulse is independent of \(z\), the distance of the pulse from fixed end of the rope. If the rope is very long the desired function for mass per unit length \(\mu (z)\) in terms of \(\mu_{0}\) [mass per unit length of the rope at the top \((z = 0)\)] is given by

1 \(\mu (z) = {\mu _0}{e^{ - \frac{{gz}}{{{v^2}}}}}\)
2 \(\mu (z) = {\mu _0}{e^{ + \frac{{gz}}{{{v^2}}}}}\)
3 \(\mu(z)=\mu_{0} \log _{e}\left(\dfrac{g}{v^{2}}\right) z\)
4 \(\mu (z) = {\mu _0}{e^{ + \left( {\frac{{{v^2}}}{{gz}}} \right)}}\)
PHXI15:WAVES

354859 Two phases in a stretched string whose centres are initially \(8\;cm\) apart are moving towards each other as shown in the figure. The speed of each pulse is \(2\;cm/s\). After 2 seconds, the total energy of the pulses will be
supporting img

1 Zero
2 Partly kinetic and partly potential
3 Purely kinetic
4 Purely potential
PHXI15:WAVES

354860 A metallic wire of \(1\,m\) length has a mass of \(10 \times {10^{ - 3}}\;kg\). If a tension of \(100\,N\) is applied to a wire, what is the speed of transverse wave ?

1 \(200\;m{s^{ - 1}}\)
2 \(100\;m{s^{ - 1}}\)
3 \(0.1\;m{s^{ - 1}}\)
4 \(10\;m{s^{ - 1}}\)
PHXI15:WAVES

354861 A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is \(v\). If a small transverse disturbance is produced at a point of the loop, speed (relative to the string) of this disturbance travel on the string is \(x v\) then \(x\) is
supporting img

1 3
2 2
3 1
4 4
PHXI15:WAVES

354858 A rope hangs from a rigid support. A pulse is set by jiggling the bottom end. We want to design a rope in which velocity \(v\) of pulse is independent of \(z\), the distance of the pulse from fixed end of the rope. If the rope is very long the desired function for mass per unit length \(\mu (z)\) in terms of \(\mu_{0}\) [mass per unit length of the rope at the top \((z = 0)\)] is given by

1 \(\mu (z) = {\mu _0}{e^{ - \frac{{gz}}{{{v^2}}}}}\)
2 \(\mu (z) = {\mu _0}{e^{ + \frac{{gz}}{{{v^2}}}}}\)
3 \(\mu(z)=\mu_{0} \log _{e}\left(\dfrac{g}{v^{2}}\right) z\)
4 \(\mu (z) = {\mu _0}{e^{ + \left( {\frac{{{v^2}}}{{gz}}} \right)}}\)
PHXI15:WAVES

354859 Two phases in a stretched string whose centres are initially \(8\;cm\) apart are moving towards each other as shown in the figure. The speed of each pulse is \(2\;cm/s\). After 2 seconds, the total energy of the pulses will be
supporting img

1 Zero
2 Partly kinetic and partly potential
3 Purely kinetic
4 Purely potential
PHXI15:WAVES

354860 A metallic wire of \(1\,m\) length has a mass of \(10 \times {10^{ - 3}}\;kg\). If a tension of \(100\,N\) is applied to a wire, what is the speed of transverse wave ?

1 \(200\;m{s^{ - 1}}\)
2 \(100\;m{s^{ - 1}}\)
3 \(0.1\;m{s^{ - 1}}\)
4 \(10\;m{s^{ - 1}}\)
PHXI15:WAVES

354861 A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is \(v\). If a small transverse disturbance is produced at a point of the loop, speed (relative to the string) of this disturbance travel on the string is \(x v\) then \(x\) is
supporting img

1 3
2 2
3 1
4 4
PHXI15:WAVES

354858 A rope hangs from a rigid support. A pulse is set by jiggling the bottom end. We want to design a rope in which velocity \(v\) of pulse is independent of \(z\), the distance of the pulse from fixed end of the rope. If the rope is very long the desired function for mass per unit length \(\mu (z)\) in terms of \(\mu_{0}\) [mass per unit length of the rope at the top \((z = 0)\)] is given by

1 \(\mu (z) = {\mu _0}{e^{ - \frac{{gz}}{{{v^2}}}}}\)
2 \(\mu (z) = {\mu _0}{e^{ + \frac{{gz}}{{{v^2}}}}}\)
3 \(\mu(z)=\mu_{0} \log _{e}\left(\dfrac{g}{v^{2}}\right) z\)
4 \(\mu (z) = {\mu _0}{e^{ + \left( {\frac{{{v^2}}}{{gz}}} \right)}}\)
PHXI15:WAVES

354859 Two phases in a stretched string whose centres are initially \(8\;cm\) apart are moving towards each other as shown in the figure. The speed of each pulse is \(2\;cm/s\). After 2 seconds, the total energy of the pulses will be
supporting img

1 Zero
2 Partly kinetic and partly potential
3 Purely kinetic
4 Purely potential
PHXI15:WAVES

354860 A metallic wire of \(1\,m\) length has a mass of \(10 \times {10^{ - 3}}\;kg\). If a tension of \(100\,N\) is applied to a wire, what is the speed of transverse wave ?

1 \(200\;m{s^{ - 1}}\)
2 \(100\;m{s^{ - 1}}\)
3 \(0.1\;m{s^{ - 1}}\)
4 \(10\;m{s^{ - 1}}\)
PHXI15:WAVES

354861 A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is \(v\). If a small transverse disturbance is produced at a point of the loop, speed (relative to the string) of this disturbance travel on the string is \(x v\) then \(x\) is
supporting img

1 3
2 2
3 1
4 4
PHXI15:WAVES

354858 A rope hangs from a rigid support. A pulse is set by jiggling the bottom end. We want to design a rope in which velocity \(v\) of pulse is independent of \(z\), the distance of the pulse from fixed end of the rope. If the rope is very long the desired function for mass per unit length \(\mu (z)\) in terms of \(\mu_{0}\) [mass per unit length of the rope at the top \((z = 0)\)] is given by

1 \(\mu (z) = {\mu _0}{e^{ - \frac{{gz}}{{{v^2}}}}}\)
2 \(\mu (z) = {\mu _0}{e^{ + \frac{{gz}}{{{v^2}}}}}\)
3 \(\mu(z)=\mu_{0} \log _{e}\left(\dfrac{g}{v^{2}}\right) z\)
4 \(\mu (z) = {\mu _0}{e^{ + \left( {\frac{{{v^2}}}{{gz}}} \right)}}\)
PHXI15:WAVES

354859 Two phases in a stretched string whose centres are initially \(8\;cm\) apart are moving towards each other as shown in the figure. The speed of each pulse is \(2\;cm/s\). After 2 seconds, the total energy of the pulses will be
supporting img

1 Zero
2 Partly kinetic and partly potential
3 Purely kinetic
4 Purely potential
PHXI15:WAVES

354860 A metallic wire of \(1\,m\) length has a mass of \(10 \times {10^{ - 3}}\;kg\). If a tension of \(100\,N\) is applied to a wire, what is the speed of transverse wave ?

1 \(200\;m{s^{ - 1}}\)
2 \(100\;m{s^{ - 1}}\)
3 \(0.1\;m{s^{ - 1}}\)
4 \(10\;m{s^{ - 1}}\)
PHXI15:WAVES

354861 A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is \(v\). If a small transverse disturbance is produced at a point of the loop, speed (relative to the string) of this disturbance travel on the string is \(x v\) then \(x\) is
supporting img

1 3
2 2
3 1
4 4