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Chapter 9: Problem 138
Water waves produced by a motorboat sailing in water are (A) neither longitudinal no transverse. (B) both longitudinal and transverse. (C) only longitudinal. (D) only transverse.
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A particle performs simple harmonic motion with amplitude \(A\). Its speed is trebled at the instant that it is at a distance \(\frac{2 A}{3}\) from equilibrium position. The new amplitude of the motion is (A) \(3 A\) (B) \(A \sqrt{3}\) (C) \(\frac{7 A}{3}\) (D) \(\frac{A}{3} \sqrt{41}\)
A mass \(M\) is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period \(T\). If the mass is increased by \(m\), the time period becomes \(\frac{5 T}{3}\). Then the radio of \(\frac{m}{M}\) is (A) \(\frac{3}{5}\) (B) \(\frac{25}{9}\) (C) \(\frac{16}{9}\) (D) \(\frac{5}{3}\)
A motor cycle starts from rest and accelerates along a straight path at \(2 \mathrm{~m} / \mathrm{s}^{2}\). At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at \(94 \%\) of its value when the motor cycle was at rest? (Speed of sound \(=330 \mathrm{~ms}^{-1}\) ) (A) \(98 \mathrm{~m}\) (B) \(147 \mathrm{~m}\) (C) \(196 \mathrm{~m}\) (D) \(49 \mathrm{~m}\)
A closed organ pipe of length \(99.4 \mathrm{~cm}\) is vibrating in its first overtone and in always resonance with a tuning fork having frequency \(f=(300-2 t) \mathrm{Hz}\), where \(t\) is time in second. The rate by which radius of organ pipe changes when its radius is \(1 \mathrm{~cm}\) is (speed of sound in organ pipe \(=320 \mathrm{~m} / \mathrm{s}\) ) (A) \(\frac{1}{72} \mathrm{~m} / \mathrm{s}\) (B) \(\frac{1}{36} \mathrm{~m} / \mathrm{s}\) (C) \(\frac{1}{18} \mathrm{~m} / \mathrm{s}\) (D) \(\frac{1}{9} \mathrm{~m} / \mathrm{s}\)
A wave disturbance in a medium is described by \(y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)\), where \(x\) and \(y\) are in meter and \(t\) is in second. Then (A) First node occurs at \(x=0.15 \mathrm{~m}\) (B) First anti-node occurs at \(x=0.3 \mathrm{~m}\) (C) The speed of interfering waves is \(5.0 \mathrm{~m} / \mathrm{s}\) (D) The wavelength is \(0.2 \mathrm{~m}\)
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