A vibrator, pulley, and hanging object are arranged as in Figure P18.219(attachment) with a compound string, consisting of two strings of different masses and lengths fastened together end-to-end. The first string, which has a mass of 1.56 g and a length of 61.0 cm, runs from the vibrator to the junction of the two strings. The second string runs from the junction over the pulley to the suspended 7.02 kg object. The mass and length of the string from the junction to the pulley are, respectively, 6.75 g and 100.3 cm. a) Find the lowest frequency for which standing waves are observed in both strings, with a node at the junction. The standing wave patterns in the two strings may have different numbers of nodes. b) What is the total number of nodes observed along the compound string at this frequency, excluding the nodes at the vibrator and the pulley?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A vibrator, pulley, and hanging object are arranged as in Figure P18.219(attachment) with a compound string, consisting of two strings of different masses and lengths fastened together end-to-end. The first string, which has a mass of 1.56 g and a length of 61.0 cm, runs from the vibrator to the junction of the two strings. The second string runs from the junction over the pulley to the suspended 7.02 kg object. The mass and length of the string from the junction to the pulley are, respectively, 6.75 g and 100.3 cm.
a) Find the lowest frequency for which standing waves are observed in both strings, with a node at the junction. The standing wave patterns in the two strings may have different numbers of nodes.
b) What is the total number of nodes observed along the compound string at this frequency, excluding the nodes at the vibrator and the pulley?
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