B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 2: CONCEPT APPLICATION EXERCISE

A source and a detector $D$ of high frequency waves are a distance $d$ apart on the ground. Maximum signal is received at $D$ when the reflecting layer is at a height $H.$ When the layer rises a distance $h,$ no signal is detected at $D.$ Neglecting absorption in the atmosphere, find the relation between $d, h, H,$ and the wavelength $\lambda$ of the waves.

Two waves have the same frequency. The first has intensity $I_0.$ The second has intensity $4{\mathrm{I}}_0$ and lags behind the first in phase by $\pi /2.$ When they meet, find the resultant intensity, and the phase relationship of the resultant wave with the first wave.

A travelling wave has speeds $50 \mathrm{m} {\mathrm{s}}^{-1}$ and $200 \mathrm{m} {\mathrm{s}}^{-1}$ in two different media $A$ and $B.$ Such a wave travelling through $A,$ gets incident normally on a plane boundary, separating $A$ and $B.$ Find the ratio of amplitudes of the reflected and transmitted waves.

The ship in figure travels along a straight line parallel to the shore and a distance $d=600 \mathrm{m}$ from it. The ship's radio receives simultaneous signals of the same frequency from antennas $A$ and $B,$ separated by a distance $L=800 \mathrm{m}.$ The signals interfere constructively at point $C,$ which is equidistant from $A$ and $B.$ The signal goes through the first minimum at point $D,$ which is directly outward from the shore from point $B.$ Determine the wavelength of the radio waves.

Two wires of different linear mass densities are soldered together end to end and then stretched under a tension $F.$ The wave speed in the first wire is thrice than in the second. If a harmonic wave travelling in the first wire is incident on the junction of the wires and if the amplitude of the incident wave is, $A=\sqrt{13} \mathrm{cm},$ find the amplitude of reflected wave.

The pulse shown in figure has a speed of $5 \mathrm{cm} {\mathrm{s}}^{-1}.$ If the linear mass density of the right string is $0.5$ that of the left string, find the ratio of the height of the transmitted pulse to that of the incident pulse.

The figure shows a tube structure in which a signal is sent from one end and is received at the other end. The frequency of the sound source can be varied electronically between, $2000$ and $5000 \mathrm{Hz}.$ Find the frequencies at which maxima of intensity are detected. The speed of sound in air, $340 \mathrm{m} {\mathrm{s}}^{-1}.$

In Quinck's acoustic interferometer, it is found that the sound intensity has a minimum value of, $100$ units at one position of the sliding tube, and continuously climbs to a maximum of $900$, units at a second position, $1.65 \mathrm{cm}$ from the first. Find

$\left(\mathrm{a}\right)$ The frequency of the sound emitted by the source and, 

$\left(\mathrm{b}\right)$ The relative amplitudes of the two waves arriving at the detector. The velocity of sound in air $=340 \mathrm{m} {\mathrm{s}}^{-1}.$