Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Stationary Waves, Exercise 4: Evaluation Test

Figure shown is part of a stationary wave between two fixed points. Which point(s) of $1$, $2$ and $3$ are in phase with point $x$?

A taut string fixed at both ends vibrates in $n^{\text {th }}$ overtone. The separation between adjacent node and antinodes is equal to $d$. Then string length is

A composite wire fixed at both ends consists of two uniform parts having length $l$ and $4 l$ and mass per unit lengths $\mu$ and $4 \mu$ respectively. Then in fundamental mode of vibration, wavelength in heavy wire, keeping junction as node, is

Assertion: Two points in adjacent loops of a string wave in the case of standing wave formation attain their maximum kinetic energy simultaneously.

Reason: The two points in the adjacent loops of standing wave are out of phase exactly by $\pi$.

A wire of identical length and cross-section is used for fixed vibration between two rigid supports slightly more than the length of strings. The wire has Young's modulus$=2Y$ and mass per unit length$=\frac{\mu }{2}$ and $v$ is the fundamental frequency. Find frequency in the $2^{\mathrm{nd}}$ mode of this wire.

Two identical point-like sound sources emitting sound in same phase of wavelength $1 \mathrm{m}$ are located at points $P$ and $Q$ as shown in figure. All sides of the polygon are equal and of length $1 \mathrm{m}$. The intensity of sound at $M$ due to source $P$ alone is $I_0$. What will be the intensity of sound at point $M$ when both the source are on?

A rope is made up of a number of identical strands twisted together. At one point, the rope becomes frayed so that only a single strand continues (See figure). The rope is held under tension and the wave of amplitude $1.0 \mathrm{cm}$ is sent from the single strand. The wave reflected back along the single strand has an amplitude of $0.45 \mathrm{cm}$. How many strands are there in the rope?

Two waves with similar frequency are added. The resulting waveform oscillates with the average frequency and with an oscillating amplitude that changes with a frequency equal the difference between the original frequencies. These oscillations in the amplitude are know as beats. The traces show the resulting waveforms that occur when two different pairs of waves are added. Graph is for the same time interval in both cases. Which of the following statements is true?