Superposition of Transverse Waves
PHXI15:WAVES

355160 The stationary waves set up on a string having the equation : \(y = (2\;mm)\sin \left[ {\left( {6.28\;{m^{ - 1}}} \right)x} \right]\cos \omega t\) The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then the smallest length of the string is

1 \(50\;cm\)
2 \(20\;cm\)
3 \(40\;cm\)
4 \(30\;cm\)
PHXI15:WAVES

355161 A wave represented by the equation \(y=a \cos (k x-\omega t)\) is superposed with another wave to form a stationary wave such that the point \(x=0\) is a node. The equation of the other wave is

1 \(-a \sin (k x-\omega t)\)
2 \(-a \cos (k x-\omega t)\)
3 \(a \sin (k x+\omega t)\)
4 \(-a \cos (k x+\omega t)\)
PHXI15:WAVES

355162 A stretched wire of length \(110\;cm\) is divided into three segments whose frequencies are in ratio 1:2:3. Their lengths must be:

1 \(20\;cm,30\;cm,60\;cm\)
2 \(60\;cm,30\;cm,20\;cm\)
3 \(60\;cm,20\;cm,30\;cm\)
4 \(30\;cm,60\;cm,20\;cm\)
PHXI15:WAVES

355163 Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is

1 \(\dfrac{1}{3}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{1}{6}\)
PHXI15:WAVES

355164 A sinusoidal wave with amplitude \(y_{m}\) is travelling with speed \(v\) on a string with linear density \(\mu\). The angular frequency of the wave is \(\omega\). Mark the one which is correct (only one parameter is changed at a time).

1 Doubling the frequency doubles the rate at which energy is carried along the string
2 If the amplitude were doubled, the rate at which energy is carried would be halved
3 If the amplitude were doubled, the rate at which energy is carried would be doubled
4 The rate at which energy is carried is directly proportional to the velocity of the wave
PHXI15:WAVES

355160 The stationary waves set up on a string having the equation : \(y = (2\;mm)\sin \left[ {\left( {6.28\;{m^{ - 1}}} \right)x} \right]\cos \omega t\) The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then the smallest length of the string is

1 \(50\;cm\)
2 \(20\;cm\)
3 \(40\;cm\)
4 \(30\;cm\)
PHXI15:WAVES

355161 A wave represented by the equation \(y=a \cos (k x-\omega t)\) is superposed with another wave to form a stationary wave such that the point \(x=0\) is a node. The equation of the other wave is

1 \(-a \sin (k x-\omega t)\)
2 \(-a \cos (k x-\omega t)\)
3 \(a \sin (k x+\omega t)\)
4 \(-a \cos (k x+\omega t)\)
PHXI15:WAVES

355162 A stretched wire of length \(110\;cm\) is divided into three segments whose frequencies are in ratio 1:2:3. Their lengths must be:

1 \(20\;cm,30\;cm,60\;cm\)
2 \(60\;cm,30\;cm,20\;cm\)
3 \(60\;cm,20\;cm,30\;cm\)
4 \(30\;cm,60\;cm,20\;cm\)
PHXI15:WAVES

355163 Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is

1 \(\dfrac{1}{3}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{1}{6}\)
PHXI15:WAVES

355164 A sinusoidal wave with amplitude \(y_{m}\) is travelling with speed \(v\) on a string with linear density \(\mu\). The angular frequency of the wave is \(\omega\). Mark the one which is correct (only one parameter is changed at a time).

1 Doubling the frequency doubles the rate at which energy is carried along the string
2 If the amplitude were doubled, the rate at which energy is carried would be halved
3 If the amplitude were doubled, the rate at which energy is carried would be doubled
4 The rate at which energy is carried is directly proportional to the velocity of the wave
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI15:WAVES

355160 The stationary waves set up on a string having the equation : \(y = (2\;mm)\sin \left[ {\left( {6.28\;{m^{ - 1}}} \right)x} \right]\cos \omega t\) The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then the smallest length of the string is

1 \(50\;cm\)
2 \(20\;cm\)
3 \(40\;cm\)
4 \(30\;cm\)
PHXI15:WAVES

355161 A wave represented by the equation \(y=a \cos (k x-\omega t)\) is superposed with another wave to form a stationary wave such that the point \(x=0\) is a node. The equation of the other wave is

1 \(-a \sin (k x-\omega t)\)
2 \(-a \cos (k x-\omega t)\)
3 \(a \sin (k x+\omega t)\)
4 \(-a \cos (k x+\omega t)\)
PHXI15:WAVES

355162 A stretched wire of length \(110\;cm\) is divided into three segments whose frequencies are in ratio 1:2:3. Their lengths must be:

1 \(20\;cm,30\;cm,60\;cm\)
2 \(60\;cm,30\;cm,20\;cm\)
3 \(60\;cm,20\;cm,30\;cm\)
4 \(30\;cm,60\;cm,20\;cm\)
PHXI15:WAVES

355163 Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is

1 \(\dfrac{1}{3}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{1}{6}\)
PHXI15:WAVES

355164 A sinusoidal wave with amplitude \(y_{m}\) is travelling with speed \(v\) on a string with linear density \(\mu\). The angular frequency of the wave is \(\omega\). Mark the one which is correct (only one parameter is changed at a time).

1 Doubling the frequency doubles the rate at which energy is carried along the string
2 If the amplitude were doubled, the rate at which energy is carried would be halved
3 If the amplitude were doubled, the rate at which energy is carried would be doubled
4 The rate at which energy is carried is directly proportional to the velocity of the wave
PHXI15:WAVES

355160 The stationary waves set up on a string having the equation : \(y = (2\;mm)\sin \left[ {\left( {6.28\;{m^{ - 1}}} \right)x} \right]\cos \omega t\) The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then the smallest length of the string is

1 \(50\;cm\)
2 \(20\;cm\)
3 \(40\;cm\)
4 \(30\;cm\)
PHXI15:WAVES

355161 A wave represented by the equation \(y=a \cos (k x-\omega t)\) is superposed with another wave to form a stationary wave such that the point \(x=0\) is a node. The equation of the other wave is

1 \(-a \sin (k x-\omega t)\)
2 \(-a \cos (k x-\omega t)\)
3 \(a \sin (k x+\omega t)\)
4 \(-a \cos (k x+\omega t)\)
PHXI15:WAVES

355162 A stretched wire of length \(110\;cm\) is divided into three segments whose frequencies are in ratio 1:2:3. Their lengths must be:

1 \(20\;cm,30\;cm,60\;cm\)
2 \(60\;cm,30\;cm,20\;cm\)
3 \(60\;cm,20\;cm,30\;cm\)
4 \(30\;cm,60\;cm,20\;cm\)
PHXI15:WAVES

355163 Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is

1 \(\dfrac{1}{3}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{1}{6}\)
PHXI15:WAVES

355164 A sinusoidal wave with amplitude \(y_{m}\) is travelling with speed \(v\) on a string with linear density \(\mu\). The angular frequency of the wave is \(\omega\). Mark the one which is correct (only one parameter is changed at a time).

1 Doubling the frequency doubles the rate at which energy is carried along the string
2 If the amplitude were doubled, the rate at which energy is carried would be halved
3 If the amplitude were doubled, the rate at which energy is carried would be doubled
4 The rate at which energy is carried is directly proportional to the velocity of the wave
PHXI15:WAVES

355160 The stationary waves set up on a string having the equation : \(y = (2\;mm)\sin \left[ {\left( {6.28\;{m^{ - 1}}} \right)x} \right]\cos \omega t\) The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then the smallest length of the string is

1 \(50\;cm\)
2 \(20\;cm\)
3 \(40\;cm\)
4 \(30\;cm\)
PHXI15:WAVES

355161 A wave represented by the equation \(y=a \cos (k x-\omega t)\) is superposed with another wave to form a stationary wave such that the point \(x=0\) is a node. The equation of the other wave is

1 \(-a \sin (k x-\omega t)\)
2 \(-a \cos (k x-\omega t)\)
3 \(a \sin (k x+\omega t)\)
4 \(-a \cos (k x+\omega t)\)
PHXI15:WAVES

355162 A stretched wire of length \(110\;cm\) is divided into three segments whose frequencies are in ratio 1:2:3. Their lengths must be:

1 \(20\;cm,30\;cm,60\;cm\)
2 \(60\;cm,30\;cm,20\;cm\)
3 \(60\;cm,20\;cm,30\;cm\)
4 \(30\;cm,60\;cm,20\;cm\)
PHXI15:WAVES

355163 Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is

1 \(\dfrac{1}{3}\)
2 \(\dfrac{1}{4}\)
3 \(\dfrac{1}{5}\)
4 \(\dfrac{1}{6}\)
PHXI15:WAVES

355164 A sinusoidal wave with amplitude \(y_{m}\) is travelling with speed \(v\) on a string with linear density \(\mu\). The angular frequency of the wave is \(\omega\). Mark the one which is correct (only one parameter is changed at a time).

1 Doubling the frequency doubles the rate at which energy is carried along the string
2 If the amplitude were doubled, the rate at which energy is carried would be halved
3 If the amplitude were doubled, the rate at which energy is carried would be doubled
4 The rate at which energy is carried is directly proportional to the velocity of the wave