The fundamental frequency for tube A with both into open is
\(V_B={V\over 2L}\)
The fundamental frequency for tube B with one end closed is
\(V_B={V\over 4L}\)
\({VA\over VB}={V/2L\over V/4L}=2\)

An echo is produced when sound reflected from a distant obstacle comes back after an interval of 1/10 second or more. In an echo, the original and reflected sounds are heard repetitively. Reverberation on the other hand connects of successive reflections which follow each other so quickly that they cannot produce separate echoes

For an echo of a simple sound to be heard, the minimum distance between speaker and the walls should be 17m. As the length of a room is less then 17m, so we do not hear on echo.

We can distinguish between longitudinal and transverse ways by performing polarization experiments. Transverse waves can be polorised while longitudinal waves cannot be poloriused.

Phase difference = \(\frac{2\pi}{\lambda}\) (path difference)
\(\Delta \varphi =\frac { 2\pi }{ \lambda } \Delta r=\frac { \lambda }{ 2\pi } \Delta \varphi \)

When a particle is in motion, the rate of change, of displacement at any instant of time is defined as velocity of the particle at that instant of time. This is known as particle velocity.

The duration for which the sound persists is called reverberation time.

In a closed room the sound is repeatedly reflected from the walls and it is even heard long after the sound source ceases to function. The residual sound remaining in an enclosure and the phenomenon of multiple reflections of sound is called reverberation.

The pitch of sound of our national animal is higher than that of mosquitos. In addition, the frequency of sound wave generated by our national animal is more than the frequency of sound wave generated by mosquitos.

"The sound power transmitted per unit area taken normal to the propagation of the sound wave". The loudness of sound is defined as "the degree of sensation of sound produced in the ear or the perception of sound by the listener".

When two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed. This phenomenon is known as beats. The number of amplitude maxima per second is called beat frequency. If we have two sources, then their difference in frequency gives the beat frequency.
Number of beats per second
n = f₁ - f₂ per second

Interference is a phenomenon in which two waves superimpose to form a resultant wave of greater, lower or the same amplitude.

This implies, when increasing the value of a, the line shifts towards right side. For a = vt, y = x − vt satisfies the differential equation. Though this function satisfies the differential equation, it is not finite for all values of x and t. Hence, it does not represent a wave.

Th e time taken by the sound to come back as echo is 2t = 4 \(\Rightarrow\) t = 2 s
\(\therefore\) Th e distance is d = vt =(343 m s^-1)(2 s) = 686 m.

(a) Bulk modulus
\(B =V\left|\frac{\Delta P}{\Delta V}\right|=\frac{100 \times 10^{3}}{0.005 \times 10^{-2}}= \)
\(=\frac{100 \times 10^{3}}{5 \times 10^{-5}}=2000 \mathrm{MPa}, \text { where }\)
MPa is mega pascal
(b) Speed of sound in water is
\(v=\sqrt { \frac { B }{ \rho } } =\sqrt { \frac { { 200\times 10 }^{ 6 } }{ 1000 } } =1414 \ ms^{-1}\)