Transverse displacement of a string clamped at its both ends is given by yleft( {x,t} right) =

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14.Waves and Sound

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The transverse displacement of a string clamped at its both ends is given by

$y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$

where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

All the points on the string between two consecutive nodes vibrate with same frequency, phase and amplitude.

All the points on the string between two consecutive nodes vibrate with same frequency and phase but different amplitude

All the points on the string between two consecutive nodes vibrate with different frequency and phase but same amplitude

All the points on the string between twoconsecutive nodes vibrate with different frequency, phase and amplitude

Solution

The given equation is

$\mathrm{y}(\mathrm{x}, \mathrm{t})=2 \sin \left(\frac{2 \pi}{3} \mathrm{x}\right) \cos (100 \pi \mathrm{t})$

It represents a stationary wave. Therefore, all the points between consecutive nodes vibrate with same frequency and same phase but different amplitude.

Standard 11

Physics

The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is …. $Hz$

easy

A wire of length $30\,cm$, stretched between rigid supports, has it's $n^{\text {th}}$ and $(n+1)^{\text {th}}$ harmonics at $400\,Hz$ and $450\; Hz$, respectively. If tension in the string is $2700\,N$, it's linear mass density is………$kg/m$.

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(JEE MAIN-2022)

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is …. $N$

hard

(AIEEE-2010)

A steel rod $100\,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel …… $km/sec$

medium

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequecny of the new pipe so obtained will be

medium

(NEET-2017)

The transverse displacement of a string clamped at its both ends is given by $y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$ where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

Solution

Similar Questions

The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is …. $Hz$

A wire of length $30\,cm$, stretched between rigid supports, has it's $n^{\text {th}}$ and $(n+1)^{\text {th}}$ harmonics at $400\,Hz$ and $450\; Hz$, respectively. If tension in the string is $2700\,N$, it's linear mass density is………$kg/m$.

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by $y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is …. $N$

A steel rod $100\,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel …… $km/sec$

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequecny of the new pipe so obtained will be

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The transverse displacement of a string clamped at its both ends is given by

$y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$

where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is …. $N$