If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be
AIPMT 1989, Medium
Download our app for free and get started
$I = 2{\pi ^2}{a^2}{n^2}$$v\rho $
$\Rightarrow$ $I \propto {a^2}{n^2}$
$\Rightarrow$ $\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{{a_1}}}{{{a_2}}}} \right)^2} \times {\left( {\frac{{{n_1}}}{{{n_2}}}} \right)^2}$
$ = {\left( {\frac{1}{2}} \right)^2} \times {\left( {\frac{1}{{1/4}}} \right)^2}$
$\Rightarrow {I_2} = \frac{{{I_1}}}{4}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement $(s)$ related to the movement of the points shown in the figure. The points of maximum rarefaction areView Solution
- 2Two sound waves of wavelength ${\lambda _1}$ and ${\lambda _2}$ $\left( {{\lambda _2} > {\lambda _1}} \right)$ produce $n\, beats/s$, the speed of sound isView Solution
- 3A student plotted the following four graphs representing the variation of velocity of sound in a gas with the pressure $P$. Which one is correctView Solution
- 4Two trains move towards each other with the same speed. The speed of sound is $340 \;m / s$. If the height of the tone of the whistle of one of them heard on the other changes $9 / 8$ times, then the speed of each train should be ........... $m/sec$View Solution
- 5A travelling harmonic wave is represented by the equation $y(x, t) = 10^{-3}\,sin\,(50t + 2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?View Solution
- 6A transverse harmonic wave on a string is given by $y(x, t)=5 \sin (6 t+0.003 x)$ where $x$ and $y$ are in $cm$ and $t$ in $sec$. The wave velocity is $...........\,ms ^{-1}$.View Solution
- 7A closed pipe of length $300 \,cm$ contains some sand. A speaker is connected at one of its ends. The frequency of the speaker at which the sand will arrange itself in $20$ equidistant piles is close to .......... $kHz$ (velocity of sound is $300 \,m / s )$View Solution
- 8Ten tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce $4$ beats per second. The highest frequency is twice that of the lowest. Possible highest and lowest frequencies (in $Hz$ ) are ................View Solution
- 9Velocity of sound in airView Solution
$I.$ Increases with temperature
$II.$ Decreases with temperature
$III.$ Increase with pressure
$IV.$ Is independent of pressure
$V.$ Is independent of temperature
Choose the correct answer.
- 10A source and a detector move away from each other in absence of wind with a speed of $20\, {m} / {s}$ with respect to the ground. If the detector detects a frequency of $1800\, {Hz}$ of the sound coming from the source, then the original frequency of source considering speed of sound in air $340\, {m} / {s}$ will be ${Hz}$View Solution