Superposition of Transverse Waves
PHXI15:WAVES

355173 An object of mass \(m\) is hung from a thin taut string (with linear mass density \(\mu=2 {~g} / {m}\) ) that passes over a light pulley as shown in figure. The string is connected to a vibrator which can be vibrated with constant frequency \(f\), and the length of the string between vibrator and the pulley is \(L=2.0 {~m}\). The standing waves are formed when the mass \(m\) of the object is either 16.0 \(kg\) or 25.0 \(kg\) . It is observed that no standing waves are formed with any mass between these values, however. What is the largest object mass for which standing waves could be observed? (Use \(g=9.8 {~m} / {s}^{2}\) )
supporting img

1 \(100\,kg\)
2 \(250\,kg\)
3 \(400\,kg\)
4 \(700\,kg\)
PHXI15:WAVES

355174 A standing wave pattern is formed on a string. One of the waves is given by equation \(y_{1}=a \sin \left(\omega t-k x+\dfrac{\pi}{3}\right)\) then the equation of the other wave such that at \(x=0\) a node is formed.

1 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
2 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
3 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{2 \pi}{3}\right)\)
4 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{4 \pi}{3}\right)\)
PHXI15:WAVES

355175 A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y(x, t)=0.5 \sin \left(\dfrac{5 \pi}{4} x\right) \cos (200 \pi t)\) What is the speed of the travelling wave moving in the positive \(x\) direction ? \(x\)and \(t\) are in meter and second, respectively.)

1 \(120\;m/s\)
2 \(90\;m/s\)
3 \(160\;m/s\)
4 \(180\;m/s\)
PHXI15:WAVES

355176 A stretched wire of length \(260\;cm\) is set into vibrations. It is divided into three segments whose frequencies are in the ratio \(2: 3: 4\). Their lengths must be

1 \(80\;cm,60\;cm,120\;cm\)
2 \(120\;cm,80\;cm,60\;cm\)
3 \(60\;cm,80\;cm,120\;cm\)
4 \(120\;cm,60\;cm,80\;cm\)
PHXI15:WAVES

355173 An object of mass \(m\) is hung from a thin taut string (with linear mass density \(\mu=2 {~g} / {m}\) ) that passes over a light pulley as shown in figure. The string is connected to a vibrator which can be vibrated with constant frequency \(f\), and the length of the string between vibrator and the pulley is \(L=2.0 {~m}\). The standing waves are formed when the mass \(m\) of the object is either 16.0 \(kg\) or 25.0 \(kg\) . It is observed that no standing waves are formed with any mass between these values, however. What is the largest object mass for which standing waves could be observed? (Use \(g=9.8 {~m} / {s}^{2}\) )
supporting img

1 \(100\,kg\)
2 \(250\,kg\)
3 \(400\,kg\)
4 \(700\,kg\)
PHXI15:WAVES

355174 A standing wave pattern is formed on a string. One of the waves is given by equation \(y_{1}=a \sin \left(\omega t-k x+\dfrac{\pi}{3}\right)\) then the equation of the other wave such that at \(x=0\) a node is formed.

1 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
2 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
3 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{2 \pi}{3}\right)\)
4 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{4 \pi}{3}\right)\)
PHXI15:WAVES

355175 A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y(x, t)=0.5 \sin \left(\dfrac{5 \pi}{4} x\right) \cos (200 \pi t)\) What is the speed of the travelling wave moving in the positive \(x\) direction ? \(x\)and \(t\) are in meter and second, respectively.)

1 \(120\;m/s\)
2 \(90\;m/s\)
3 \(160\;m/s\)
4 \(180\;m/s\)
PHXI15:WAVES

355176 A stretched wire of length \(260\;cm\) is set into vibrations. It is divided into three segments whose frequencies are in the ratio \(2: 3: 4\). Their lengths must be

1 \(80\;cm,60\;cm,120\;cm\)
2 \(120\;cm,80\;cm,60\;cm\)
3 \(60\;cm,80\;cm,120\;cm\)
4 \(120\;cm,60\;cm,80\;cm\)
PHXI15:WAVES

355173 An object of mass \(m\) is hung from a thin taut string (with linear mass density \(\mu=2 {~g} / {m}\) ) that passes over a light pulley as shown in figure. The string is connected to a vibrator which can be vibrated with constant frequency \(f\), and the length of the string between vibrator and the pulley is \(L=2.0 {~m}\). The standing waves are formed when the mass \(m\) of the object is either 16.0 \(kg\) or 25.0 \(kg\) . It is observed that no standing waves are formed with any mass between these values, however. What is the largest object mass for which standing waves could be observed? (Use \(g=9.8 {~m} / {s}^{2}\) )
supporting img

1 \(100\,kg\)
2 \(250\,kg\)
3 \(400\,kg\)
4 \(700\,kg\)
PHXI15:WAVES

355174 A standing wave pattern is formed on a string. One of the waves is given by equation \(y_{1}=a \sin \left(\omega t-k x+\dfrac{\pi}{3}\right)\) then the equation of the other wave such that at \(x=0\) a node is formed.

1 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
2 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
3 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{2 \pi}{3}\right)\)
4 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{4 \pi}{3}\right)\)
PHXI15:WAVES

355175 A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y(x, t)=0.5 \sin \left(\dfrac{5 \pi}{4} x\right) \cos (200 \pi t)\) What is the speed of the travelling wave moving in the positive \(x\) direction ? \(x\)and \(t\) are in meter and second, respectively.)

1 \(120\;m/s\)
2 \(90\;m/s\)
3 \(160\;m/s\)
4 \(180\;m/s\)
PHXI15:WAVES

355176 A stretched wire of length \(260\;cm\) is set into vibrations. It is divided into three segments whose frequencies are in the ratio \(2: 3: 4\). Their lengths must be

1 \(80\;cm,60\;cm,120\;cm\)
2 \(120\;cm,80\;cm,60\;cm\)
3 \(60\;cm,80\;cm,120\;cm\)
4 \(120\;cm,60\;cm,80\;cm\)
PHXI15:WAVES

355173 An object of mass \(m\) is hung from a thin taut string (with linear mass density \(\mu=2 {~g} / {m}\) ) that passes over a light pulley as shown in figure. The string is connected to a vibrator which can be vibrated with constant frequency \(f\), and the length of the string between vibrator and the pulley is \(L=2.0 {~m}\). The standing waves are formed when the mass \(m\) of the object is either 16.0 \(kg\) or 25.0 \(kg\) . It is observed that no standing waves are formed with any mass between these values, however. What is the largest object mass for which standing waves could be observed? (Use \(g=9.8 {~m} / {s}^{2}\) )
supporting img

1 \(100\,kg\)
2 \(250\,kg\)
3 \(400\,kg\)
4 \(700\,kg\)
PHXI15:WAVES

355174 A standing wave pattern is formed on a string. One of the waves is given by equation \(y_{1}=a \sin \left(\omega t-k x+\dfrac{\pi}{3}\right)\) then the equation of the other wave such that at \(x=0\) a node is formed.

1 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
2 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{\pi}{3}\right)\)
3 \(y_{2}=a \sin \left(\omega t+k x+\dfrac{2 \pi}{3}\right)\)
4 \(y_{2}=a \cos \left(\omega t+k x+\dfrac{4 \pi}{3}\right)\)
PHXI15:WAVES

355175 A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y(x, t)=0.5 \sin \left(\dfrac{5 \pi}{4} x\right) \cos (200 \pi t)\) What is the speed of the travelling wave moving in the positive \(x\) direction ? \(x\)and \(t\) are in meter and second, respectively.)

1 \(120\;m/s\)
2 \(90\;m/s\)
3 \(160\;m/s\)
4 \(180\;m/s\)
PHXI15:WAVES

355176 A stretched wire of length \(260\;cm\) is set into vibrations. It is divided into three segments whose frequencies are in the ratio \(2: 3: 4\). Their lengths must be

1 \(80\;cm,60\;cm,120\;cm\)
2 \(120\;cm,80\;cm,60\;cm\)
3 \(60\;cm,80\;cm,120\;cm\)
4 \(120\;cm,60\;cm,80\;cm\)
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