Variation of Intensity in Space

Q. Figure shows two coherent line sources of sound, $S_1$ and $S_2$ separated by a distance $12\text{m}$. The sources emit same power and their wavelengths are also same. A detector moves along a circular path with centre at $S_2$ and radius $4\text{m}$. The wavelength of the sound is $1\text{m}$. When it is at $‘A^{\prime }$ the intensity of sound is $I_o=25{\text{W/m}}^2$. The intensity of sound (in $W/m^2$) at $B$ due to $S_1$ only is (Take $S_1\text{A=9 m}$)

1. $9$
2. $4$
3. $\frac{9}{\sqrt{10}}$
4. None of these

Q. A sound wave of frequency $f$ travels horizontal to the right. It is reflected from a large vertical plane surface moving to left with a speed $v$. If the speed of sound in medium is $c$ then

1. The number of the beats heard by a stationary listner to the left of the reflecting surface is $\frac{vf}{c-v}$
2. The wavelength of reflected wave is $\frac{c}{f}\left(\frac{c-v}{c+v}\right)$
3. The number of waves striking the plane surface per second is $f\left(\frac{c+v}{c}\right)$
4. The frequency of the reflected wave is $f\left(\frac{c+v}{c-v}\right)$

Q. A stretched wire fixed at both ends is oscillating in the third overtone mode. Equation of the transverse stationary wave produced in this wire is $y=A\sin \left(6\pi x\right)\sin \left(20\pi t\right)$ ($x$ is in $\text{m}$ and $t$ in $\text{seconds}$). Find the length of the wire.

1. $\frac{2}{3}\text{m}$
2. $\frac{4}{3}\text{m}$
3. $\frac{3}{4}\text{m}$
4. $\frac{3}{2}\text{m}$

Q. Two vibrating strings made of the same material but of lengths $L$ and $2L$ have the radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes-the one of length $L$ with frequency $v_1$ and the other with frequency $v_2.$ The ratio $\frac{v_1}{v_2}$ is equal to

1. $4$
2. $1$
3. $8$
4. $2$

Q. Figure shows two coherent line sources of sound, $S_1$ and $S_2$ separated by a distance $12\text{m}$. The sources emit same power and their wavelengths are also same. A detector moves along a circular path with centre at $S_2$ and radius $4\text{m}$. The wavelength of the sound is $1\text{m}$. When it is at $‘A^{\prime }$ the intensity of sound is $I_o=25{\text{W/m}}^2$. The intensity of sound (in $W/m^2$) at $B$ due to $S_1$ only is (Take $S_1\text{A=9 m}$)

1. $9$
2. $4$
3. $\frac{9}{\sqrt{10}}$
4. None of these