The fundamental frequency of a closed organ pipe of a length $20$ cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

A wave traveling in the +ve $x\text-$direction having maximum displacement along $y\text-$direction as $1~\text{m}$, wavelength $2\pi~\text{m}$ and frequency of $\frac{1}{\pi}~\text{Hz}$, is represented by:

The driver of a car travelling at a speed of 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by the driver is:

1. 550 Hz

2. 555.5 Hz

3. 720 Hz

4. 500 Hz

Two sound waves with wavelengths $5.0~\text{m}$ and $5.5~\text{m}$, respectively, propagate in gas with a velocity of $330~\text{m/s}$. How many beats per second can we expect?
1. $12$
2. $0$
3. $1$
4. $6$

A transverse wave propagating along the $x\text-$axis is represented by:
$y(x,t)=8.0\sin\left(0.5\pi x-4\pi t-\frac{\pi}{4}\right)$, where $x$ is in meters and $t$ in seconds. The speed of the wave is: 
1. $4\pi$ m/s
2. $0.5$ m/s
3. $\frac{\pi}{4}$ m/s
4. $8$ m/s