Consider a rope fixed at both ends under tension so that it is horizontal (i.e. assume the rope is along x-axis, with gravity acting along z-axis). Now the right end is continually oscillated at high frequency n (say n=100 Hz) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travells along the rope and is reflected at the left end. Let the total length of rope be l, total mass be m and the acceleration due to gravity be g. After initial phase (say a mintue or so), the rope has __(BLANK-1)__ wave, which is __(BLANK-2)__ in nature. It results from superposition of left travelling and right travelling __(BLANK-3)__ waves. This resulting wave has a frequency __ (BLANK-4)_ that of oscillation frequency nu. Simple dimensional analysis indicates that the frequency of can be of the form: ___(BLANK-5)__ .
The tension applied to a metal wire of one metre length produces an elastic strain of 1%. The density of the metal is \( 8000 \, kg/m^3 \) and Young's modulus of the metal is \( 2 \times 10^{11} \, Nm^{-2} \). The fundamental frequency of the transverse waves in the metal wire is:
Figure shows a part of an electric circuit. The potentials at points \( a, b, \text{and} \, c \) are \( 30 \, \text{V}, 12 \, \text{V}, \, \text{and} \, 2 \, \text{V} \), respectively. The current through the \( 20 \, \Omega \) resistor will be: