Characteristics of Progressive Waves
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PHXI15:WAVES

354536 The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-(\sqrt{c} x+\sqrt{d} t)^{2}}\). This represents a

1 Standing wave of frequency \(\sqrt{c}\)
2 Standing wave of frequency \(\dfrac{1}{\sqrt{d}}\)
3 Wave moving in \(+x\)-direction with speed \(\sqrt{\dfrac{c}{d}}\)
4 Wave moving in - \(x\)-direction with speed \(\sqrt{\dfrac{d}{c}}\)
PHXI15:WAVES

354537 The transverse displacement of a wave on a string is given by \(y(x, t)=e^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b x} x t\right)}\).
This represents a:

1 Standing wave of frequency \(\sqrt{b}\)
2 Wave moving in -\(x\) direction with speed
\(\sqrt{\dfrac{b}{a}}\)
3 Wave moving \( + x\) direction with speed \(\sqrt{\dfrac{a}{b}}\)
4 Standing wave of frequency \(\dfrac{1}{\sqrt{b}}\)
PHXI15:WAVES

354538 A long string having a cross-sectional area \(0.80\;m{m^2}\) and density \(12.5\;g/c{m^3}\) is subjected to a tension of \(64\;N\) along the positive \(x\)-axis. One end (at \(x=0\) ) of this string is attached to a vibrator moving in transverse direction at a frequency of \(20\;Hz\) At \(t = 0\), the source is at a maximum displacement \(y = 1.0\;cm\).
Write the equation for the wave

1 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{2}{m^{ - 1}}} \right)x} \right\}} \right]\)
2 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{2}\;{m^{ - 1}}} \right)x} \right\}} \right]\)
3 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
4 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
PHXI15:WAVES

354539 Assertion :
A wave of frequency \(500\;Hz\) is propagating with a velocity of \(350\;m{s^{ - 1}}\).
Distance between two particles with \(60^{\circ}\) phase difference is \(12\;cm\).
Reason :
\(x=\dfrac{\lambda}{2 \pi} \phi\).

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

354540 The equation of a wave is \(y=5 \sin \left(\dfrac{t}{0.04}-\dfrac{x}{4}\right)\), where \(x\) is in \(cm\) and \(t\) is in second. The maximum velocity of the wave will be

1 \(1\;m{s^{ - 1}}\)
2 \(2\;m{s^{ - 1}}\)
3 \(1.5\;m{s^{ - 1}}\)
4 \(1.25\;m{s^{ - 1}}\)
NEET DIGITAL LIBRARY
PHXI15:WAVES

354536 The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-(\sqrt{c} x+\sqrt{d} t)^{2}}\). This represents a

1 Standing wave of frequency \(\sqrt{c}\)
2 Standing wave of frequency \(\dfrac{1}{\sqrt{d}}\)
3 Wave moving in \(+x\)-direction with speed \(\sqrt{\dfrac{c}{d}}\)
4 Wave moving in - \(x\)-direction with speed \(\sqrt{\dfrac{d}{c}}\)
PHXI15:WAVES

354537 The transverse displacement of a wave on a string is given by \(y(x, t)=e^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b x} x t\right)}\).
This represents a:

1 Standing wave of frequency \(\sqrt{b}\)
2 Wave moving in -\(x\) direction with speed
\(\sqrt{\dfrac{b}{a}}\)
3 Wave moving \( + x\) direction with speed \(\sqrt{\dfrac{a}{b}}\)
4 Standing wave of frequency \(\dfrac{1}{\sqrt{b}}\)
PHXI15:WAVES

354538 A long string having a cross-sectional area \(0.80\;m{m^2}\) and density \(12.5\;g/c{m^3}\) is subjected to a tension of \(64\;N\) along the positive \(x\)-axis. One end (at \(x=0\) ) of this string is attached to a vibrator moving in transverse direction at a frequency of \(20\;Hz\) At \(t = 0\), the source is at a maximum displacement \(y = 1.0\;cm\).
Write the equation for the wave

1 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{2}{m^{ - 1}}} \right)x} \right\}} \right]\)
2 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{2}\;{m^{ - 1}}} \right)x} \right\}} \right]\)
3 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
4 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
PHXI15:WAVES

354539 Assertion :
A wave of frequency \(500\;Hz\) is propagating with a velocity of \(350\;m{s^{ - 1}}\).
Distance between two particles with \(60^{\circ}\) phase difference is \(12\;cm\).
Reason :
\(x=\dfrac{\lambda}{2 \pi} \phi\).

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

354540 The equation of a wave is \(y=5 \sin \left(\dfrac{t}{0.04}-\dfrac{x}{4}\right)\), where \(x\) is in \(cm\) and \(t\) is in second. The maximum velocity of the wave will be

1 \(1\;m{s^{ - 1}}\)
2 \(2\;m{s^{ - 1}}\)
3 \(1.5\;m{s^{ - 1}}\)
4 \(1.25\;m{s^{ - 1}}\)
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PHXI15:WAVES

354536 The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-(\sqrt{c} x+\sqrt{d} t)^{2}}\). This represents a

1 Standing wave of frequency \(\sqrt{c}\)
2 Standing wave of frequency \(\dfrac{1}{\sqrt{d}}\)
3 Wave moving in \(+x\)-direction with speed \(\sqrt{\dfrac{c}{d}}\)
4 Wave moving in - \(x\)-direction with speed \(\sqrt{\dfrac{d}{c}}\)
PHXI15:WAVES

354537 The transverse displacement of a wave on a string is given by \(y(x, t)=e^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b x} x t\right)}\).
This represents a:

1 Standing wave of frequency \(\sqrt{b}\)
2 Wave moving in -\(x\) direction with speed
\(\sqrt{\dfrac{b}{a}}\)
3 Wave moving \( + x\) direction with speed \(\sqrt{\dfrac{a}{b}}\)
4 Standing wave of frequency \(\dfrac{1}{\sqrt{b}}\)
PHXI15:WAVES

354538 A long string having a cross-sectional area \(0.80\;m{m^2}\) and density \(12.5\;g/c{m^3}\) is subjected to a tension of \(64\;N\) along the positive \(x\)-axis. One end (at \(x=0\) ) of this string is attached to a vibrator moving in transverse direction at a frequency of \(20\;Hz\) At \(t = 0\), the source is at a maximum displacement \(y = 1.0\;cm\).
Write the equation for the wave

1 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{2}{m^{ - 1}}} \right)x} \right\}} \right]\)
2 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{2}\;{m^{ - 1}}} \right)x} \right\}} \right]\)
3 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
4 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
PHXI15:WAVES

354539 Assertion :
A wave of frequency \(500\;Hz\) is propagating with a velocity of \(350\;m{s^{ - 1}}\).
Distance between two particles with \(60^{\circ}\) phase difference is \(12\;cm\).
Reason :
\(x=\dfrac{\lambda}{2 \pi} \phi\).

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

354540 The equation of a wave is \(y=5 \sin \left(\dfrac{t}{0.04}-\dfrac{x}{4}\right)\), where \(x\) is in \(cm\) and \(t\) is in second. The maximum velocity of the wave will be

1 \(1\;m{s^{ - 1}}\)
2 \(2\;m{s^{ - 1}}\)
3 \(1.5\;m{s^{ - 1}}\)
4 \(1.25\;m{s^{ - 1}}\)
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PHXI15:WAVES

354536 The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-(\sqrt{c} x+\sqrt{d} t)^{2}}\). This represents a

1 Standing wave of frequency \(\sqrt{c}\)
2 Standing wave of frequency \(\dfrac{1}{\sqrt{d}}\)
3 Wave moving in \(+x\)-direction with speed \(\sqrt{\dfrac{c}{d}}\)
4 Wave moving in - \(x\)-direction with speed \(\sqrt{\dfrac{d}{c}}\)
PHXI15:WAVES

354537 The transverse displacement of a wave on a string is given by \(y(x, t)=e^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b x} x t\right)}\).
This represents a:

1 Standing wave of frequency \(\sqrt{b}\)
2 Wave moving in -\(x\) direction with speed
\(\sqrt{\dfrac{b}{a}}\)
3 Wave moving \( + x\) direction with speed \(\sqrt{\dfrac{a}{b}}\)
4 Standing wave of frequency \(\dfrac{1}{\sqrt{b}}\)
PHXI15:WAVES

354538 A long string having a cross-sectional area \(0.80\;m{m^2}\) and density \(12.5\;g/c{m^3}\) is subjected to a tension of \(64\;N\) along the positive \(x\)-axis. One end (at \(x=0\) ) of this string is attached to a vibrator moving in transverse direction at a frequency of \(20\;Hz\) At \(t = 0\), the source is at a maximum displacement \(y = 1.0\;cm\).
Write the equation for the wave

1 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{2}{m^{ - 1}}} \right)x} \right\}} \right]\)
2 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{2}\;{m^{ - 1}}} \right)x} \right\}} \right]\)
3 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
4 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
PHXI15:WAVES

354539 Assertion :
A wave of frequency \(500\;Hz\) is propagating with a velocity of \(350\;m{s^{ - 1}}\).
Distance between two particles with \(60^{\circ}\) phase difference is \(12\;cm\).
Reason :
\(x=\dfrac{\lambda}{2 \pi} \phi\).

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

354540 The equation of a wave is \(y=5 \sin \left(\dfrac{t}{0.04}-\dfrac{x}{4}\right)\), where \(x\) is in \(cm\) and \(t\) is in second. The maximum velocity of the wave will be

1 \(1\;m{s^{ - 1}}\)
2 \(2\;m{s^{ - 1}}\)
3 \(1.5\;m{s^{ - 1}}\)
4 \(1.25\;m{s^{ - 1}}\)
NEET DIGITAL LIBRARY
PHXI15:WAVES

354536 The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-(\sqrt{c} x+\sqrt{d} t)^{2}}\). This represents a

1 Standing wave of frequency \(\sqrt{c}\)
2 Standing wave of frequency \(\dfrac{1}{\sqrt{d}}\)
3 Wave moving in \(+x\)-direction with speed \(\sqrt{\dfrac{c}{d}}\)
4 Wave moving in - \(x\)-direction with speed \(\sqrt{\dfrac{d}{c}}\)
PHXI15:WAVES

354537 The transverse displacement of a wave on a string is given by \(y(x, t)=e^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b x} x t\right)}\).
This represents a:

1 Standing wave of frequency \(\sqrt{b}\)
2 Wave moving in -\(x\) direction with speed
\(\sqrt{\dfrac{b}{a}}\)
3 Wave moving \( + x\) direction with speed \(\sqrt{\dfrac{a}{b}}\)
4 Standing wave of frequency \(\dfrac{1}{\sqrt{b}}\)
PHXI15:WAVES

354538 A long string having a cross-sectional area \(0.80\;m{m^2}\) and density \(12.5\;g/c{m^3}\) is subjected to a tension of \(64\;N\) along the positive \(x\)-axis. One end (at \(x=0\) ) of this string is attached to a vibrator moving in transverse direction at a frequency of \(20\;Hz\) At \(t = 0\), the source is at a maximum displacement \(y = 1.0\;cm\).
Write the equation for the wave

1 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{2}{m^{ - 1}}} \right)x} \right\}} \right]\)
2 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{2}\;{m^{ - 1}}} \right)x} \right\}} \right]\)
3 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t - \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
4 \(y = (1.0\;cm)\cos \left[ {\left( {40\pi {s^{ - 1}}} \right)t + \left\{ {\left( {\frac{\pi }{4}{m^{ - 1}}} \right)x} \right\}} \right]\)
PHXI15:WAVES

354539 Assertion :
A wave of frequency \(500\;Hz\) is propagating with a velocity of \(350\;m{s^{ - 1}}\).
Distance between two particles with \(60^{\circ}\) phase difference is \(12\;cm\).
Reason :
\(x=\dfrac{\lambda}{2 \pi} \phi\).

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

354540 The equation of a wave is \(y=5 \sin \left(\dfrac{t}{0.04}-\dfrac{x}{4}\right)\), where \(x\) is in \(cm\) and \(t\) is in second. The maximum velocity of the wave will be

1 \(1\;m{s^{ - 1}}\)
2 \(2\;m{s^{ - 1}}\)
3 \(1.5\;m{s^{ - 1}}\)
4 \(1.25\;m{s^{ - 1}}\)