Superposition of Transverse Waves
PHXI15:WAVES

355143 A uniform wire of length \(L\), diameter \(D\) and density \(\rho\) is stretched under a tension \(T\). The correct relation between its fundamental frequency \(f\), the length \(L\) and the diameter \(D\) is

1 \(f \propto \dfrac{1}{L D}\)
2 \(f \propto \dfrac{1}{L \sqrt{D}}\)
3 \(f \propto \dfrac{1}{D^{2}}\)
4 \(f \propto \dfrac{1}{L D^{2}}\)
PHXI15:WAVES

355144 A string in a musical instrument is \(50\,cm\) long and its fundamental frequency is \(800\;Hz\). If a frequency of \(1000\;Hz\) is to be produced, then required length of string is:

1 \(37.5\;cm\)
2 \(40\;cm\)
3 \(50\;cm\)
4 \(62.5\;cm\)
PHXI15:WAVES

355145 Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities \(\rho\) and \(2 \rho\). Each string is fixed at both ends. If \(f_{1}\) represents the fundamental mode of vibration of the one made with density \(\rho\) and \(f_{2}\) for another, then \(f_{1} / f_{2}\) is

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

355146 A wave travelling along uniform string represented by \(Y=A \sin (\omega t-k x)\) is superimposed on another wave travelling along the same string represented by \(Y=A \sin (\omega t+k x)\). The resultant is

1 a wave travelling along \(+x\) direction.
2 a standing wave having nodes at \(x=\left(n-\dfrac{1}{2}\right) \dfrac{\lambda}{2}\), where \(n=1,2,3, \ldots \ldots \ldots\).
3 a wave travelling along \(-x\) direction.
4 a standing wave having nodes at \(x=\dfrac{n \lambda}{2}\), where \(n=0,1,2, \ldots \ldots \ldots \ldots \ldots\).
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI15:WAVES

355143 A uniform wire of length \(L\), diameter \(D\) and density \(\rho\) is stretched under a tension \(T\). The correct relation between its fundamental frequency \(f\), the length \(L\) and the diameter \(D\) is

1 \(f \propto \dfrac{1}{L D}\)
2 \(f \propto \dfrac{1}{L \sqrt{D}}\)
3 \(f \propto \dfrac{1}{D^{2}}\)
4 \(f \propto \dfrac{1}{L D^{2}}\)
PHXI15:WAVES

355144 A string in a musical instrument is \(50\,cm\) long and its fundamental frequency is \(800\;Hz\). If a frequency of \(1000\;Hz\) is to be produced, then required length of string is:

1 \(37.5\;cm\)
2 \(40\;cm\)
3 \(50\;cm\)
4 \(62.5\;cm\)
PHXI15:WAVES

355145 Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities \(\rho\) and \(2 \rho\). Each string is fixed at both ends. If \(f_{1}\) represents the fundamental mode of vibration of the one made with density \(\rho\) and \(f_{2}\) for another, then \(f_{1} / f_{2}\) is

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

355146 A wave travelling along uniform string represented by \(Y=A \sin (\omega t-k x)\) is superimposed on another wave travelling along the same string represented by \(Y=A \sin (\omega t+k x)\). The resultant is

1 a wave travelling along \(+x\) direction.
2 a standing wave having nodes at \(x=\left(n-\dfrac{1}{2}\right) \dfrac{\lambda}{2}\), where \(n=1,2,3, \ldots \ldots \ldots\).
3 a wave travelling along \(-x\) direction.
4 a standing wave having nodes at \(x=\dfrac{n \lambda}{2}\), where \(n=0,1,2, \ldots \ldots \ldots \ldots \ldots\).
PHXI15:WAVES

355143 A uniform wire of length \(L\), diameter \(D\) and density \(\rho\) is stretched under a tension \(T\). The correct relation between its fundamental frequency \(f\), the length \(L\) and the diameter \(D\) is

1 \(f \propto \dfrac{1}{L D}\)
2 \(f \propto \dfrac{1}{L \sqrt{D}}\)
3 \(f \propto \dfrac{1}{D^{2}}\)
4 \(f \propto \dfrac{1}{L D^{2}}\)
PHXI15:WAVES

355144 A string in a musical instrument is \(50\,cm\) long and its fundamental frequency is \(800\;Hz\). If a frequency of \(1000\;Hz\) is to be produced, then required length of string is:

1 \(37.5\;cm\)
2 \(40\;cm\)
3 \(50\;cm\)
4 \(62.5\;cm\)
PHXI15:WAVES

355145 Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities \(\rho\) and \(2 \rho\). Each string is fixed at both ends. If \(f_{1}\) represents the fundamental mode of vibration of the one made with density \(\rho\) and \(f_{2}\) for another, then \(f_{1} / f_{2}\) is

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

355146 A wave travelling along uniform string represented by \(Y=A \sin (\omega t-k x)\) is superimposed on another wave travelling along the same string represented by \(Y=A \sin (\omega t+k x)\). The resultant is

1 a wave travelling along \(+x\) direction.
2 a standing wave having nodes at \(x=\left(n-\dfrac{1}{2}\right) \dfrac{\lambda}{2}\), where \(n=1,2,3, \ldots \ldots \ldots\).
3 a wave travelling along \(-x\) direction.
4 a standing wave having nodes at \(x=\dfrac{n \lambda}{2}\), where \(n=0,1,2, \ldots \ldots \ldots \ldots \ldots\).
PHXI15:WAVES

355143 A uniform wire of length \(L\), diameter \(D\) and density \(\rho\) is stretched under a tension \(T\). The correct relation between its fundamental frequency \(f\), the length \(L\) and the diameter \(D\) is

1 \(f \propto \dfrac{1}{L D}\)
2 \(f \propto \dfrac{1}{L \sqrt{D}}\)
3 \(f \propto \dfrac{1}{D^{2}}\)
4 \(f \propto \dfrac{1}{L D^{2}}\)
PHXI15:WAVES

355144 A string in a musical instrument is \(50\,cm\) long and its fundamental frequency is \(800\;Hz\). If a frequency of \(1000\;Hz\) is to be produced, then required length of string is:

1 \(37.5\;cm\)
2 \(40\;cm\)
3 \(50\;cm\)
4 \(62.5\;cm\)
PHXI15:WAVES

355145 Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities \(\rho\) and \(2 \rho\). Each string is fixed at both ends. If \(f_{1}\) represents the fundamental mode of vibration of the one made with density \(\rho\) and \(f_{2}\) for another, then \(f_{1} / f_{2}\) is

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

355146 A wave travelling along uniform string represented by \(Y=A \sin (\omega t-k x)\) is superimposed on another wave travelling along the same string represented by \(Y=A \sin (\omega t+k x)\). The resultant is

1 a wave travelling along \(+x\) direction.
2 a standing wave having nodes at \(x=\left(n-\dfrac{1}{2}\right) \dfrac{\lambda}{2}\), where \(n=1,2,3, \ldots \ldots \ldots\).
3 a wave travelling along \(-x\) direction.
4 a standing wave having nodes at \(x=\dfrac{n \lambda}{2}\), where \(n=0,1,2, \ldots \ldots \ldots \ldots \ldots\).
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