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Chapter 9: Problem 116
The range of frequencies allotted for FM radio is (A) 88 to \(108 \mathrm{kHz}\) (B) 88 to \(108 \mathrm{MHz}\) (C) 47 to \(230 \mathrm{kHz}\) (D) 47 to \(230 \mathrm{MHz}\)
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The equation of a wave on a string of linear mass density \(0.04 \mathrm{~kg} \mathrm{~m}^{-1}\) is given by $$ y=0.02(m) \sin \left[2 \pi\left(\frac{t}{0.04(s)}-\frac{x}{0.50(m)}\right)\right] \text {. The ten- } $$ sion in the string is (A) \(4.0 \mathrm{~N}\) (B) \(12.5 \mathrm{~N}\) (C) \(0.5 \mathrm{~N}\) (D) \(6.25 \mathrm{~N}\)
For a particular mode of vibration of string, the distance between two consecutive nodes is \(18 \mathrm{~cm}\). For the next higher mode, the distance becomes \(16 \mathrm{~cm}\). The length of the string is (A) \(18 \mathrm{~cm}\) (B) \(16 \mathrm{~cm}\) (C) \(144 \mathrm{~cm}\) (D) \(72 \mathrm{~cm}\)
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 \(0.2 \mathrm{~m}\)
From a single source, two wave trains sent in two different strings of same length. String-2 is four times heavy than string- 1 . The two wave equations are (area of cross-section and tension of both strings is same). \(y_{1}=A \sin \left(\omega_{1} t-k_{1} x\right)\) and \(y_{2}=2 A \sin \left(\omega_{2} t-k_{2} x\right)\) Suppose \(u=\) energy density \(P=\) power transmitted, and \(I=\) intensity of wave, \(v=\) velocity of wave, then match the following: Column-I (A) \(\frac{u_{1}}{u_{2}}=\) (B) \(\frac{P_{1}}{P_{2}}=\) (C) \(\frac{v_{1}}{v_{2}}=\) (D) \(\frac{k_{1}}{k_{2}}=\) Column-II 1\. \(\frac{1}{8}\) 2\. \(\frac{1}{16}\) 3\. 2 4\. \(\frac{1}{2}\) \(5.5\)
A signal of \(5 \mathrm{kHz}\) frequency is amplitude modulated on a carrier wave of frequency \(2 \mathrm{MHz}\). The frequencies of the resulting signal is/are (A) \(2005 \mathrm{kHz}\), and \(1995 \mathrm{kHz}\) (B) \(2005 \mathrm{kHz}, 2000 \mathrm{kHz}\) and \(1995 \mathrm{kHz}\) (C) \(2000 \mathrm{kHz}\) and \(1995 \mathrm{kHz}\) (D) \(2 \mathrm{MHz}\) only
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