172327
A transverse wave is represented by $\mathrm{y}=\mathrm{A}$ sin $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1 $\pi \mathrm{A} / 2$
2 $\pi \mathrm{A}$
3 $2 \pi \mathrm{A}$
4 $\mathrm{A}$
Explanation:
C Equation of the transverse wave is given by, $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ Wave velocity $\mathrm{v}_{\text {wave }}=f \lambda$ $\mathrm{v}_{\text {wave }}=\frac{\omega}{2 \pi} \times \lambda$ Maximum particle velocity $\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }=\mathrm{A} \omega$ $\mathrm{v}_{\text {wave }}=\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }$ $\frac{\omega \lambda}{2 \pi}=\mathrm{A} \omega$ $\lambda=2 \pi \mathrm{A}$
AIPMT-2010
WAVES
172328
Three waves of equal frequency but amplitudes $10 \mu \mathrm{m}, 4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\pi / 2$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by
1 7
2 6
3 5
4 4
Explanation:
C Given that $\mathrm{A}_{1}=10 \mu \mathrm{m} \text { Phase }$ $\mathrm{A}_{2}=4 \mu \mathrm{m} \mathrm{A}_{2}=\pi / 2$ $\mathrm{~A}_{3}=7 \mu \mathrm{m} \mathrm{A}_{3}=\pi / 2+\pi / 2=\pi$ By phase diagram method, $\mathrm{A}^{2}=(4)^{2}+(3)^{2}$ $\mathrm{~A}^{2}=25$ $\mathrm{~A}=5 \mu \mathrm{m}$
AMU-2006
WAVES
172329
The equation of a transverse wave is given by the relation $y=100 \sin \pi(0.04 z-2 t)$, where $y$ and $z$ are in $\mathrm{cm}$ and $t$ is in seconds. The frequency of this wave is
1 $1 \mathrm{~Hz}$
2 $4 \mathrm{~Hz}$
3 $25 \mathrm{~Hz}$
4 $100 \mathrm{~Hz}$.
Explanation:
A The Equation of a transverse wave is given by $y=100 \sin \pi(0.04 z-2 t)$ $y=100 \sin (0.04 \pi z-2 \pi t)$ Standard equation given by $\mathrm{y}=\mathrm{A} \sin (\mathrm{kz}-\omega \mathrm{t})$ on comparing equation (i) and equation (ii) $\omega=2 \pi$ $2 \pi f=2 \pi$ $f=1 \mathrm{~Hz}$
AMU-2003
WAVES
172330
The equation of a wave travelling in a string is given by $y=3 \cos \pi(100 t-x)$. Its wavelength is
1 $3 \mathrm{~cm}$
2 $100 \mathrm{~cm}$
3 $2 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Explanation:
C Given equation $y=3 \cos \pi(100 t-x)$ $y=3 \cos (100 \pi t-\pi x)$ Standard equation for wave $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$ $\mathrm{k}=\pi$ we know that, $\mathrm{k}=\frac{2 \pi}{\lambda}$ $\lambda=\frac{2 \pi}{\mathrm{k}} \quad(\because \mathrm{k}=\pi)$ $\lambda=\frac{2 \pi}{\pi}=2 \mathrm{~cm}$
AMU-2002
WAVES
172331
A progressive wave in a medium is represented by the equation $y=0.1 \sin \left(10 \pi t-\frac{5}{11} \pi x\right)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The wavelength and velocity of the wave is :
172327
A transverse wave is represented by $\mathrm{y}=\mathrm{A}$ sin $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1 $\pi \mathrm{A} / 2$
2 $\pi \mathrm{A}$
3 $2 \pi \mathrm{A}$
4 $\mathrm{A}$
Explanation:
C Equation of the transverse wave is given by, $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ Wave velocity $\mathrm{v}_{\text {wave }}=f \lambda$ $\mathrm{v}_{\text {wave }}=\frac{\omega}{2 \pi} \times \lambda$ Maximum particle velocity $\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }=\mathrm{A} \omega$ $\mathrm{v}_{\text {wave }}=\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }$ $\frac{\omega \lambda}{2 \pi}=\mathrm{A} \omega$ $\lambda=2 \pi \mathrm{A}$
AIPMT-2010
WAVES
172328
Three waves of equal frequency but amplitudes $10 \mu \mathrm{m}, 4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\pi / 2$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by
1 7
2 6
3 5
4 4
Explanation:
C Given that $\mathrm{A}_{1}=10 \mu \mathrm{m} \text { Phase }$ $\mathrm{A}_{2}=4 \mu \mathrm{m} \mathrm{A}_{2}=\pi / 2$ $\mathrm{~A}_{3}=7 \mu \mathrm{m} \mathrm{A}_{3}=\pi / 2+\pi / 2=\pi$ By phase diagram method, $\mathrm{A}^{2}=(4)^{2}+(3)^{2}$ $\mathrm{~A}^{2}=25$ $\mathrm{~A}=5 \mu \mathrm{m}$
AMU-2006
WAVES
172329
The equation of a transverse wave is given by the relation $y=100 \sin \pi(0.04 z-2 t)$, where $y$ and $z$ are in $\mathrm{cm}$ and $t$ is in seconds. The frequency of this wave is
1 $1 \mathrm{~Hz}$
2 $4 \mathrm{~Hz}$
3 $25 \mathrm{~Hz}$
4 $100 \mathrm{~Hz}$.
Explanation:
A The Equation of a transverse wave is given by $y=100 \sin \pi(0.04 z-2 t)$ $y=100 \sin (0.04 \pi z-2 \pi t)$ Standard equation given by $\mathrm{y}=\mathrm{A} \sin (\mathrm{kz}-\omega \mathrm{t})$ on comparing equation (i) and equation (ii) $\omega=2 \pi$ $2 \pi f=2 \pi$ $f=1 \mathrm{~Hz}$
AMU-2003
WAVES
172330
The equation of a wave travelling in a string is given by $y=3 \cos \pi(100 t-x)$. Its wavelength is
1 $3 \mathrm{~cm}$
2 $100 \mathrm{~cm}$
3 $2 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Explanation:
C Given equation $y=3 \cos \pi(100 t-x)$ $y=3 \cos (100 \pi t-\pi x)$ Standard equation for wave $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$ $\mathrm{k}=\pi$ we know that, $\mathrm{k}=\frac{2 \pi}{\lambda}$ $\lambda=\frac{2 \pi}{\mathrm{k}} \quad(\because \mathrm{k}=\pi)$ $\lambda=\frac{2 \pi}{\pi}=2 \mathrm{~cm}$
AMU-2002
WAVES
172331
A progressive wave in a medium is represented by the equation $y=0.1 \sin \left(10 \pi t-\frac{5}{11} \pi x\right)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The wavelength and velocity of the wave is :
172327
A transverse wave is represented by $\mathrm{y}=\mathrm{A}$ sin $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1 $\pi \mathrm{A} / 2$
2 $\pi \mathrm{A}$
3 $2 \pi \mathrm{A}$
4 $\mathrm{A}$
Explanation:
C Equation of the transverse wave is given by, $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ Wave velocity $\mathrm{v}_{\text {wave }}=f \lambda$ $\mathrm{v}_{\text {wave }}=\frac{\omega}{2 \pi} \times \lambda$ Maximum particle velocity $\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }=\mathrm{A} \omega$ $\mathrm{v}_{\text {wave }}=\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }$ $\frac{\omega \lambda}{2 \pi}=\mathrm{A} \omega$ $\lambda=2 \pi \mathrm{A}$
AIPMT-2010
WAVES
172328
Three waves of equal frequency but amplitudes $10 \mu \mathrm{m}, 4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\pi / 2$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by
1 7
2 6
3 5
4 4
Explanation:
C Given that $\mathrm{A}_{1}=10 \mu \mathrm{m} \text { Phase }$ $\mathrm{A}_{2}=4 \mu \mathrm{m} \mathrm{A}_{2}=\pi / 2$ $\mathrm{~A}_{3}=7 \mu \mathrm{m} \mathrm{A}_{3}=\pi / 2+\pi / 2=\pi$ By phase diagram method, $\mathrm{A}^{2}=(4)^{2}+(3)^{2}$ $\mathrm{~A}^{2}=25$ $\mathrm{~A}=5 \mu \mathrm{m}$
AMU-2006
WAVES
172329
The equation of a transverse wave is given by the relation $y=100 \sin \pi(0.04 z-2 t)$, where $y$ and $z$ are in $\mathrm{cm}$ and $t$ is in seconds. The frequency of this wave is
1 $1 \mathrm{~Hz}$
2 $4 \mathrm{~Hz}$
3 $25 \mathrm{~Hz}$
4 $100 \mathrm{~Hz}$.
Explanation:
A The Equation of a transverse wave is given by $y=100 \sin \pi(0.04 z-2 t)$ $y=100 \sin (0.04 \pi z-2 \pi t)$ Standard equation given by $\mathrm{y}=\mathrm{A} \sin (\mathrm{kz}-\omega \mathrm{t})$ on comparing equation (i) and equation (ii) $\omega=2 \pi$ $2 \pi f=2 \pi$ $f=1 \mathrm{~Hz}$
AMU-2003
WAVES
172330
The equation of a wave travelling in a string is given by $y=3 \cos \pi(100 t-x)$. Its wavelength is
1 $3 \mathrm{~cm}$
2 $100 \mathrm{~cm}$
3 $2 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Explanation:
C Given equation $y=3 \cos \pi(100 t-x)$ $y=3 \cos (100 \pi t-\pi x)$ Standard equation for wave $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$ $\mathrm{k}=\pi$ we know that, $\mathrm{k}=\frac{2 \pi}{\lambda}$ $\lambda=\frac{2 \pi}{\mathrm{k}} \quad(\because \mathrm{k}=\pi)$ $\lambda=\frac{2 \pi}{\pi}=2 \mathrm{~cm}$
AMU-2002
WAVES
172331
A progressive wave in a medium is represented by the equation $y=0.1 \sin \left(10 \pi t-\frac{5}{11} \pi x\right)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The wavelength and velocity of the wave is :
172327
A transverse wave is represented by $\mathrm{y}=\mathrm{A}$ sin $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1 $\pi \mathrm{A} / 2$
2 $\pi \mathrm{A}$
3 $2 \pi \mathrm{A}$
4 $\mathrm{A}$
Explanation:
C Equation of the transverse wave is given by, $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ Wave velocity $\mathrm{v}_{\text {wave }}=f \lambda$ $\mathrm{v}_{\text {wave }}=\frac{\omega}{2 \pi} \times \lambda$ Maximum particle velocity $\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }=\mathrm{A} \omega$ $\mathrm{v}_{\text {wave }}=\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }$ $\frac{\omega \lambda}{2 \pi}=\mathrm{A} \omega$ $\lambda=2 \pi \mathrm{A}$
AIPMT-2010
WAVES
172328
Three waves of equal frequency but amplitudes $10 \mu \mathrm{m}, 4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\pi / 2$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by
1 7
2 6
3 5
4 4
Explanation:
C Given that $\mathrm{A}_{1}=10 \mu \mathrm{m} \text { Phase }$ $\mathrm{A}_{2}=4 \mu \mathrm{m} \mathrm{A}_{2}=\pi / 2$ $\mathrm{~A}_{3}=7 \mu \mathrm{m} \mathrm{A}_{3}=\pi / 2+\pi / 2=\pi$ By phase diagram method, $\mathrm{A}^{2}=(4)^{2}+(3)^{2}$ $\mathrm{~A}^{2}=25$ $\mathrm{~A}=5 \mu \mathrm{m}$
AMU-2006
WAVES
172329
The equation of a transverse wave is given by the relation $y=100 \sin \pi(0.04 z-2 t)$, where $y$ and $z$ are in $\mathrm{cm}$ and $t$ is in seconds. The frequency of this wave is
1 $1 \mathrm{~Hz}$
2 $4 \mathrm{~Hz}$
3 $25 \mathrm{~Hz}$
4 $100 \mathrm{~Hz}$.
Explanation:
A The Equation of a transverse wave is given by $y=100 \sin \pi(0.04 z-2 t)$ $y=100 \sin (0.04 \pi z-2 \pi t)$ Standard equation given by $\mathrm{y}=\mathrm{A} \sin (\mathrm{kz}-\omega \mathrm{t})$ on comparing equation (i) and equation (ii) $\omega=2 \pi$ $2 \pi f=2 \pi$ $f=1 \mathrm{~Hz}$
AMU-2003
WAVES
172330
The equation of a wave travelling in a string is given by $y=3 \cos \pi(100 t-x)$. Its wavelength is
1 $3 \mathrm{~cm}$
2 $100 \mathrm{~cm}$
3 $2 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Explanation:
C Given equation $y=3 \cos \pi(100 t-x)$ $y=3 \cos (100 \pi t-\pi x)$ Standard equation for wave $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$ $\mathrm{k}=\pi$ we know that, $\mathrm{k}=\frac{2 \pi}{\lambda}$ $\lambda=\frac{2 \pi}{\mathrm{k}} \quad(\because \mathrm{k}=\pi)$ $\lambda=\frac{2 \pi}{\pi}=2 \mathrm{~cm}$
AMU-2002
WAVES
172331
A progressive wave in a medium is represented by the equation $y=0.1 \sin \left(10 \pi t-\frac{5}{11} \pi x\right)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The wavelength and velocity of the wave is :
172327
A transverse wave is represented by $\mathrm{y}=\mathrm{A}$ sin $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1 $\pi \mathrm{A} / 2$
2 $\pi \mathrm{A}$
3 $2 \pi \mathrm{A}$
4 $\mathrm{A}$
Explanation:
C Equation of the transverse wave is given by, $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ Wave velocity $\mathrm{v}_{\text {wave }}=f \lambda$ $\mathrm{v}_{\text {wave }}=\frac{\omega}{2 \pi} \times \lambda$ Maximum particle velocity $\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }=\mathrm{A} \omega$ $\mathrm{v}_{\text {wave }}=\left(\mathrm{v}_{\mathrm{P}}\right)_{\max }$ $\frac{\omega \lambda}{2 \pi}=\mathrm{A} \omega$ $\lambda=2 \pi \mathrm{A}$
AIPMT-2010
WAVES
172328
Three waves of equal frequency but amplitudes $10 \mu \mathrm{m}, 4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\pi / 2$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by
1 7
2 6
3 5
4 4
Explanation:
C Given that $\mathrm{A}_{1}=10 \mu \mathrm{m} \text { Phase }$ $\mathrm{A}_{2}=4 \mu \mathrm{m} \mathrm{A}_{2}=\pi / 2$ $\mathrm{~A}_{3}=7 \mu \mathrm{m} \mathrm{A}_{3}=\pi / 2+\pi / 2=\pi$ By phase diagram method, $\mathrm{A}^{2}=(4)^{2}+(3)^{2}$ $\mathrm{~A}^{2}=25$ $\mathrm{~A}=5 \mu \mathrm{m}$
AMU-2006
WAVES
172329
The equation of a transverse wave is given by the relation $y=100 \sin \pi(0.04 z-2 t)$, where $y$ and $z$ are in $\mathrm{cm}$ and $t$ is in seconds. The frequency of this wave is
1 $1 \mathrm{~Hz}$
2 $4 \mathrm{~Hz}$
3 $25 \mathrm{~Hz}$
4 $100 \mathrm{~Hz}$.
Explanation:
A The Equation of a transverse wave is given by $y=100 \sin \pi(0.04 z-2 t)$ $y=100 \sin (0.04 \pi z-2 \pi t)$ Standard equation given by $\mathrm{y}=\mathrm{A} \sin (\mathrm{kz}-\omega \mathrm{t})$ on comparing equation (i) and equation (ii) $\omega=2 \pi$ $2 \pi f=2 \pi$ $f=1 \mathrm{~Hz}$
AMU-2003
WAVES
172330
The equation of a wave travelling in a string is given by $y=3 \cos \pi(100 t-x)$. Its wavelength is
1 $3 \mathrm{~cm}$
2 $100 \mathrm{~cm}$
3 $2 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Explanation:
C Given equation $y=3 \cos \pi(100 t-x)$ $y=3 \cos (100 \pi t-\pi x)$ Standard equation for wave $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$ $\mathrm{k}=\pi$ we know that, $\mathrm{k}=\frac{2 \pi}{\lambda}$ $\lambda=\frac{2 \pi}{\mathrm{k}} \quad(\because \mathrm{k}=\pi)$ $\lambda=\frac{2 \pi}{\pi}=2 \mathrm{~cm}$
AMU-2002
WAVES
172331
A progressive wave in a medium is represented by the equation $y=0.1 \sin \left(10 \pi t-\frac{5}{11} \pi x\right)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The wavelength and velocity of the wave is :
