Waves practice · Mixed difficulty

A wave travelling along the x-axis is described by the equation $y\left( {x,t} \right) = 0.005\,\,\,cos\left( {\alpha x - \beta t} \right)$. If the wavelength and the time period of the wave are $0.08{\mkern 1mu} {\mkern 1mu} \,\,m\,\,\,and\,\,2.0{\mkern 1mu} {\mkern 1mu} s$, respectively, than $\alpha \,\,and\,\beta$ in appropriate unit are

A progressive wave travels in a medium $M_1$ and enters into another medium $M_2$ in which its speed decreases to $75 \%$. What is the ratio of the amplitude and intensity of the

a. Reflected and the incident waves, and

b. Transmitted and the incident waves?

A sonometer wire has a length $114 \mathrm{~cm}$ between two fixed ends. Where should two bridges be placed, so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1: 3: 4$ ?

Which of the following is not true for the progressive wave $y=4 \sin 2 \pi\left(\frac{t}{0.02}-\frac{x}{100}\right)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in second?

Two identical sinusoidal waves each of amplitudes 5 mm with a phase difference of $\frac{\pi }{2}$ are travelling in the same direction in a string. The amplitude of the resultant wave (in mm) is