Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 2: Exercise - 2

A metallic wire of length $l$ is held between two supports under some tension. The wire is cooled through $\mathrm{\theta }°$. Let $Y$ be Young's modulus, $\rho$ the density and $\alpha$ the thermal coefficient of linear expansion of the material of the wire. Therefore, the frequency of oscillations of the wire varies as

When a sound wave is reflected from a wall, the phase difference between the reflected and incident pressure wave is:

The wave-function for a certain standing wave on a string fixed at both ends is $y(x, t)=0.5\sin (0.025\pi x)\cos 500t$ where $x$ and $y$ are in centimeters and $t$ is in seconds. The shortest possible length of the string is:

Following are equations of four waves :

(i) $y_1=a\sin \mathrm{\omega }\left(t-\frac{\mathit{x}}{\mathit{\nu }}\right)$ (ii) $y_2 =a\cos \mathrm{\omega }\left(t+\frac{\mathit{x}}{\mathit{\nu }}\right)$ (iii) $z_1 =a\sin \mathrm{\omega }\left(t-\frac{\mathit{x}}{\mathit{\nu }}\right)$ (iv) $z_2 =a\cos \mathrm{\omega }\left(t+\frac{\mathit{x}}{\mathit{\nu }}\right)$

Which of the following statements is/are correct?

A wave disturbance in a medium is described by $y(x\mathit{,}\mathit{ }t) = 0.02 \cos (50 \pi t+ \frac{\mathrm{\pi }}{2}) \cos 10\left(\pi x\right)$, where $x$ and $y$ are in meter and $t$ in second.

The vibrations of a string of length $600 \mathrm{cm}$ fixed at both ends are represented by the equation

$y= 4 \sin \left(\mathrm{\pi } \frac{x}{15}\right) \cos (96 \mathrm{\pi }t)$

where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in seconds.

A wave given by $\mathrm{\zeta }=10\sin [ 80\pi t– 4\pi x]$ propagates in a wire of length $1 \mathrm{m}$ fixed at both ends. If another wave of similar amplitude is superimposed on this wave to produce a stationary wave then

Consider an element of a stretched string along which a wave travels. During its transverse oscillatory motion, the element passes through a point at $y=0$ and reaches its maximum at $y= y_{\mathrm{m}}$. Then, the string element has its maximum