A is singing a note and at the same time B is | vedclass

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

Question

(D) The energy $E$ of a sound wave is given by the relation $E \propto a^2 n^2$,where $a$ is the amplitude and $n$ is the frequency.Since the energies

Vedclass · Accepted Answer

Eight times as that of $A$

Vedclass · Answer

(D) The energy $E$ of a sound wave is given by the relation $E \propto a^2 n^2$,where $a$ is the amplitude and $n$ is the frequency.Since the energies of the two sounds are equal,we have $E_A = E_B$.Therefore,$a_A^2 n_A^2 = a_B^2 n_B^2$.Given that the frequency of $B$ is one-eighth the frequency of $A$,we have $n_B = \frac{1}{8} n_A$,or $\frac{n_A}{n_B} = 8$.Rearranging the energy equation: $\frac{a_B^2}{a_A^2} = \frac{n_A^2}{n_B^2}$.Taking the square root on both sides: $\frac{a_B}{a_A} = \frac{n_A}{n_B} = 8$.Thus,$a_B = 8 a_A$.The amplitude of the note of $B$ is eight times that of $A$.

$A$ is singing a note and at the same time $B$ is singing a note with exactly one-eighth the frequency of the note of $A$. If the energies of the two sounds are equal,the amplitude of the note of $B$ is:

Similar Questions

The intensity level at a distance of $200 \ cm$ from a sound source is $80 \ dB$. If there is no loss of acoustic power in the air and the threshold intensity of hearing is $10^{-12} \ W/m^2$,what is the intensity level at a distance of $400 \ cm$ from the source (in $dB$)?

$A$ string of mass $100 \, g$ is clamped between two rigid supports. $A$ wave of amplitude $2 \, mm$ is generated in the string. If the angular frequency of the wave is $5000 \, rad/s$,then the total energy of the wave in the string is ..... $J$.

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.

If the ratio of the amplitude of two waves is $4 : 3$,then the ratio of their maximum and minimum intensity will be:

If the amplitude of waves at a distance $r$ from a point source is $A$,the amplitude at a distance $2r$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module