**Question:**

Statement – 1 : Two longitudinal waves given by equations: $y_{1}(x, t)=2 a \sin (\omega t-k x)$ and $y_{2}(x, t)=a$ $\sin (2 \omega t-2 k x)$ will have equal intensity. Statement – 2: Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

Correct Option: 1

**Solution:**

### Related Questions

Assume that the displacement $(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement $(s)$ further depends on the speed of sound $(v)$, density of air $(\rho)$ and the frequency $(f)$. If $\Delta p \sim$ $10 \mathrm{~Pa}, v \sim 300 \mathrm{~m} / \mathrm{s}, \rho \sim 1 \mathrm{~kg} / \mathrm{m}^{3}$ and $f \sim 1000 \mathrm{~Hz}$, then $s$ will be of the order of (take the multiplicative constant to be 1 )

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \mathrm{~m}$, while the distance between one crest and one trough is $1.5 \mathrm{~m}$. The possible wavelengths (in $\mathrm{m}$ ) of the waves are :

A progressive wave travelling along the positive $x$-direction is represented by $y(x, t)=\operatorname{Asin}(k x-\omega t+\phi)$. Its snapshot at $t=0$ is given in the figure.

For this wave, the phase $\phi$ is:

A small speaker delivers $2 \mathrm{~W}$ of audio output. At what distance from the speaker will one detect $120 \mathrm{~dB}$ intensity sound? [Given reference intensity of sound as $10^{-12} \mathrm{~W} / \mathrm{m}^{2}$ ]

The pressure wave, $P=0.01 \sin [1000 t-3 x] \mathrm{Nm}^{-2}$, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0^{\circ} \mathrm{C}$. On some other day when temperature is $T$, the speed of sound produced by the same blade and at the same frequency is found to be $336 \mathrm{~ms}^{-1}$. Approximate value of $\mathrm{T}$ is :

A travelling harmonic wave is represented by the equation $y(x, \mathrm{t})=10^{-3} \sin (50 \mathrm{t}+2 x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

A transverse wave is represented by $y=\frac{10}{\pi} \sin \left(\frac{2 \pi}{T} t-\frac{2 \pi}{\lambda} x\right)$

For what value of the wavelength the wave velocity is twice the maximum particle velocity?

In a transverse wave the distance between a crest and neighbouring trough at the same instant is $4.0 \mathrm{~cm}$ and the distance between a crest and trough at the same place is $1.0 \mathrm{~cm}$. The next crest appears at the same place after a time interval of $0.4 \mathrm{~s}$. The maximum speed of the vibrating particles in the medium is :

When two sound waves travel in the same direction in a medium, the displacements of a particle located at ‘ $x$ ‘ at time ‘ $t$ ‘ is given by:

\begin{aligned}

&y_{1}=0.05 \cos (0.50 \pi x-100 \pi t) \\

&y_{2}=0.05 \cos (0.46 \pi x-92 \pi t)

\end{aligned}

where $y_{1}, y_{2}$ and $x$ are in meters and $t$ in seconds. The speed of sound in the medium is :

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y=\frac{1}{1+x^{2}}$ at time $t=0$ and by $y=\frac{1}{\left[1+(x-1)^{2}\right]}$ at $t=2 \mathrm{~s}$, where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in $\mathrm{m} / \mathrm{s}$ is