Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 3: Exercise-3

Determine resultant amplitude (in $\mathrm{mm}$) after super position of given four waves with help of phasor diagram.

$y_1=16\sin \omega t \mathrm{mm}, y_2=3\sin \left(\omega t-\frac{\pi }{2}\right)\mathrm{mm}, y_3=7\sin \left(\omega t+\frac{\pi }{2}\right)\mathrm{mm}$ & $y_4=-13\sin \omega t\mathrm{mm}$

Calculate the ratio of intensity of wave train $A$ to wave train $B$

In the given figure the string has mass $4.5 \mathrm{g}$. If the time taken by a transverse pulse produced at the floor to reach the pulley is $10\mathrm{p}$ ms then $\mathrm{p}$ is : $\left(g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$.

A string vibrate according to the equation $y=5\sin \left(\frac{\pi x}{3}\right)\cos \left(40\pi t\right)$ where $x$ and $y$ are in $\mathrm{cm}\text{'}s$ and $t$ is in second.

A bat emits ultrasonic sound of frequency $1000\mathrm{kHz}$ in air. If the sound meets a water surface, and the wavelength (in $\mathrm{SI}$ unit) of the reflected sound is $\lambda$ then find the value of  $\frac{50000\lambda }{17}$. The speed of sound in air is$340{ \mathrm{m} \mathrm{s}}^{-1}$and in water$1486{ \mathrm{m} \mathrm{s}}^{-1}$.

A steel rod $100 \mathrm{cm}$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.50\mathrm{kHz}$. If speed of sound in steel is $\mathrm{v} \mathrm{km} {\mathrm{s}}^{-1}$ then $\mathrm{v}$ is ?

A sonometer wire under tension of $64 \mathrm{N}$ vibrating in its fundamental mode is in resonance with a vibrating tuning fork. The vibrating portion of the sonometer wire has a length of $10 \mathrm{cm}$ and mass of $1 \mathrm{g}$, The vibrating tuning fork is now moved away from the vibrating wire with a constant speed and an observer standing near the sonometer hears one beat per second. Calculate the speed (in $\mathrm{cm} {\mathrm{s}}^{-1}$) with which the tuning fork is moved, if the speed of sound in air is $300 \mathrm{m} {\mathrm{s}}^{-1}$.