Superposition of Transverse Waves
PHXI15:WAVES

355057 A transverse harmonic wave is propagating along a taut string. Tension in the string is 50 \(N\) and its linear mass density is \(0.02 {~kg} {~m}^{-1}\). The string is driven by an 80 \(Hz\) oscillator tied to one end oscillating with an amplitude of 1 \(mm\) . The other end of the string is terminated so that all the wave energy is absorbed and there is no reflection. Calculate the average energy of the wave (in \(mJ\) ) on a 1.0 \(m\) long segment of the string. (Use \(\pi^{2}=10\) )

1 \(1.27\,mJ\)
2 \(2.56\,mJ\)
3 \(5.62\,mJ\)
4 \(8.25\,mJ\)
PHXI15:WAVES

355058 Assertion :
The phase difference between two medium particles having a path difference \(\lambda\) is \(2 \pi\).
Reason :
The phase difference is directly proportional to path difference of a particle.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355059 Statement A :
On reflection from a rigid boundary there takes place a complete reversal of phase.
Statement B :
On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI15:WAVES

355060 The equation of a plane progressive wave is
\(y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)\)
When it is reflected at rigid supports, its amplitude becomes \({(2 / 3)^{\text {rd }}}\) of its previous value. The equation of the reflected wave is

1 \({y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
2 \({y=0.06 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
3 \({y=0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
4 \({y=-0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
PHXI15:WAVES

355061 Equation of plane progressive wave is given by \(y=0.6 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\). On reflection from a denser medium its amplitude becomes \(2 / 3\) of the amplitude of the incident wave. The equation of the reflected wave is

1 \(y=0.6 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
2 \(y=-0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
3 \(y=0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
4 \(y=-0.4 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\)
PHXI15:WAVES

355057 A transverse harmonic wave is propagating along a taut string. Tension in the string is 50 \(N\) and its linear mass density is \(0.02 {~kg} {~m}^{-1}\). The string is driven by an 80 \(Hz\) oscillator tied to one end oscillating with an amplitude of 1 \(mm\) . The other end of the string is terminated so that all the wave energy is absorbed and there is no reflection. Calculate the average energy of the wave (in \(mJ\) ) on a 1.0 \(m\) long segment of the string. (Use \(\pi^{2}=10\) )

1 \(1.27\,mJ\)
2 \(2.56\,mJ\)
3 \(5.62\,mJ\)
4 \(8.25\,mJ\)
PHXI15:WAVES

355058 Assertion :
The phase difference between two medium particles having a path difference \(\lambda\) is \(2 \pi\).
Reason :
The phase difference is directly proportional to path difference of a particle.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355059 Statement A :
On reflection from a rigid boundary there takes place a complete reversal of phase.
Statement B :
On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI15:WAVES

355060 The equation of a plane progressive wave is
\(y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)\)
When it is reflected at rigid supports, its amplitude becomes \({(2 / 3)^{\text {rd }}}\) of its previous value. The equation of the reflected wave is

1 \({y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
2 \({y=0.06 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
3 \({y=0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
4 \({y=-0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
PHXI15:WAVES

355061 Equation of plane progressive wave is given by \(y=0.6 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\). On reflection from a denser medium its amplitude becomes \(2 / 3\) of the amplitude of the incident wave. The equation of the reflected wave is

1 \(y=0.6 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
2 \(y=-0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
3 \(y=0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
4 \(y=-0.4 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\)
PHXI15:WAVES

355057 A transverse harmonic wave is propagating along a taut string. Tension in the string is 50 \(N\) and its linear mass density is \(0.02 {~kg} {~m}^{-1}\). The string is driven by an 80 \(Hz\) oscillator tied to one end oscillating with an amplitude of 1 \(mm\) . The other end of the string is terminated so that all the wave energy is absorbed and there is no reflection. Calculate the average energy of the wave (in \(mJ\) ) on a 1.0 \(m\) long segment of the string. (Use \(\pi^{2}=10\) )

1 \(1.27\,mJ\)
2 \(2.56\,mJ\)
3 \(5.62\,mJ\)
4 \(8.25\,mJ\)
PHXI15:WAVES

355058 Assertion :
The phase difference between two medium particles having a path difference \(\lambda\) is \(2 \pi\).
Reason :
The phase difference is directly proportional to path difference of a particle.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355059 Statement A :
On reflection from a rigid boundary there takes place a complete reversal of phase.
Statement B :
On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI15:WAVES

355060 The equation of a plane progressive wave is
\(y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)\)
When it is reflected at rigid supports, its amplitude becomes \({(2 / 3)^{\text {rd }}}\) of its previous value. The equation of the reflected wave is

1 \({y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
2 \({y=0.06 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
3 \({y=0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
4 \({y=-0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
PHXI15:WAVES

355061 Equation of plane progressive wave is given by \(y=0.6 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\). On reflection from a denser medium its amplitude becomes \(2 / 3\) of the amplitude of the incident wave. The equation of the reflected wave is

1 \(y=0.6 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
2 \(y=-0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
3 \(y=0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
4 \(y=-0.4 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\)
PHXI15:WAVES

355057 A transverse harmonic wave is propagating along a taut string. Tension in the string is 50 \(N\) and its linear mass density is \(0.02 {~kg} {~m}^{-1}\). The string is driven by an 80 \(Hz\) oscillator tied to one end oscillating with an amplitude of 1 \(mm\) . The other end of the string is terminated so that all the wave energy is absorbed and there is no reflection. Calculate the average energy of the wave (in \(mJ\) ) on a 1.0 \(m\) long segment of the string. (Use \(\pi^{2}=10\) )

1 \(1.27\,mJ\)
2 \(2.56\,mJ\)
3 \(5.62\,mJ\)
4 \(8.25\,mJ\)
PHXI15:WAVES

355058 Assertion :
The phase difference between two medium particles having a path difference \(\lambda\) is \(2 \pi\).
Reason :
The phase difference is directly proportional to path difference of a particle.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355059 Statement A :
On reflection from a rigid boundary there takes place a complete reversal of phase.
Statement B :
On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI15:WAVES

355060 The equation of a plane progressive wave is
\(y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)\)
When it is reflected at rigid supports, its amplitude becomes \({(2 / 3)^{\text {rd }}}\) of its previous value. The equation of the reflected wave is

1 \({y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
2 \({y=0.06 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
3 \({y=0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
4 \({y=-0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
PHXI15:WAVES

355061 Equation of plane progressive wave is given by \(y=0.6 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\). On reflection from a denser medium its amplitude becomes \(2 / 3\) of the amplitude of the incident wave. The equation of the reflected wave is

1 \(y=0.6 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
2 \(y=-0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
3 \(y=0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
4 \(y=-0.4 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\)
PHXI15:WAVES

355057 A transverse harmonic wave is propagating along a taut string. Tension in the string is 50 \(N\) and its linear mass density is \(0.02 {~kg} {~m}^{-1}\). The string is driven by an 80 \(Hz\) oscillator tied to one end oscillating with an amplitude of 1 \(mm\) . The other end of the string is terminated so that all the wave energy is absorbed and there is no reflection. Calculate the average energy of the wave (in \(mJ\) ) on a 1.0 \(m\) long segment of the string. (Use \(\pi^{2}=10\) )

1 \(1.27\,mJ\)
2 \(2.56\,mJ\)
3 \(5.62\,mJ\)
4 \(8.25\,mJ\)
PHXI15:WAVES

355058 Assertion :
The phase difference between two medium particles having a path difference \(\lambda\) is \(2 \pi\).
Reason :
The phase difference is directly proportional to path difference of a particle.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355059 Statement A :
On reflection from a rigid boundary there takes place a complete reversal of phase.
Statement B :
On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
PHXI15:WAVES

355060 The equation of a plane progressive wave is
\(y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)\)
When it is reflected at rigid supports, its amplitude becomes \({(2 / 3)^{\text {rd }}}\) of its previous value. The equation of the reflected wave is

1 \({y=0.09 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
2 \({y=0.06 \sin 8 \pi\left(t-\dfrac{x}{20}\right)}\)
3 \({y=0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
4 \({y=-0.06 \sin 8 \pi\left(t+\dfrac{x}{20}\right)}\)
PHXI15:WAVES

355061 Equation of plane progressive wave is given by \(y=0.6 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\). On reflection from a denser medium its amplitude becomes \(2 / 3\) of the amplitude of the incident wave. The equation of the reflected wave is

1 \(y=0.6 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
2 \(y=-0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
3 \(y=0.4 \sin 2 \pi\left(t+\dfrac{x}{2}\right)\)
4 \(y=-0.4 \sin 2 \pi\left(t-\dfrac{x}{2}\right)\)