A point source is kept at the center of a sph | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The volume of a sphere is given by $V = \frac{4}{3} \pi R^3$, which implies $V \propto R^3$.If the volume $V$ increases by $8$ times, then $R^3$ i

Vedclass · Accepted Answer

decrease by $4$ times

Vedclass · Answer

(D) The volume of a sphere is given by $V = \frac{4}{3} \pi R^3$, which implies $V \propto R^3$.If the volume $V$ increases by $8$ times, then $R^3$ increases by $8$ times, so the radius $R$ increases by $2$ times $(R \rightarrow 2R)$.The surface area of the sphere is $A = 4 \pi R^2$, which implies $A \propto R^2$.Since $R$ increases by $2$ times, the area $A$ increases by $2^2 = 4$ times $(A \rightarrow 4A)$.Intensity $I$ is defined as power per unit area, $I = \frac{P}{A}$.Since the power $P$ of the point source remains constant, $I \propto \frac{1}{A}$.Therefore, if the area $A$ increases by $4$ times, the intensity $I$ will decrease by $4$ times $(I \rightarrow \frac{I}{4})$.

$A$ point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by $8$ times, the intensity will

Similar Questions

The relation between time and displacement for two particles is given by
${y_1} = 0.06 \sin 2\pi (1.04t + {\phi _1})$
${y_2} = 0.03 \sin 2\pi (1.04t + {\phi _2})$
The ratio of the intensity of the waves produced by the vibrations of the two particles will be

If the separation between the screen and the source is increased by $2\%$,what would be the effect on the intensity?

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure. The ratio of their intensities $I_A/I_B$ is equal to:

Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.
Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

Consider ten identical sources of sound,all emitting the same frequency but having random phase angles. If the average intensity of each source is $I_0$,what will be the average resultant intensity $I$ due to all these ten sources?

Vedclass Test Series

Exam Paper Generator

Online Exam Module