(A) Let $d$ be the distance between the firecracker and the boat.The sound travels through water with speed $u$ and through air with speed $v$.The tim

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(A) Let $d$ be the distance between the firecracker and the boat.The sound travels through water with speed $u$ and through air with speed $v$.The time taken for sound to reach the boat through water is $t_1 = \frac{d}{u}$.The time taken for sound to reach the boat through air is $t_2 = \frac{d}{v}$.Given that the time interval between the two sounds is $t$,we have $t_2 - t_1 = t$ (since $v t_1$).Substituting the expressions: $\frac{d}{v} - \frac{d}{u} = t$.Factor out $d$: $d \left( \frac{u - v}{uv} \right) = t$.Solving for $d$: $d = \frac{uvt}{u - v}$.

Class 11 Physics Waves and Sound Sound Waves (Longitudinal wave) and it’s Characteristics (Speed etc.)

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$A$ firecracker exploding on the surface of a lake is heard as two sounds a time interval $t$ apart by a man on a boat close to the water surface. Sound travels with a speed $u$ in water and a speed $v$ in air. The distance from the exploding firecracker to the boat is

A
$\frac{uvt}{u - v}$
B
$\frac{t(u + v)}{uv}$
C
$\frac{t(u - v)}{uv}$
D
$\frac{uvt}{u + v}$

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Waves and Sound

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Sound Waves (Longitudinal wave) and it’s Characteristics (Speed etc.)

The 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 are

Medium

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$A$ sound wave of frequency $160 \,Hz$ has a velocity of $320 \,m/s$. When it travels through air, the particles having a phase difference of $90^{\circ}$ are separated by a distance of: (in $cm$)

DifficultMHT CET 2021

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$A$ granite rod of $60 \ cm$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^3 \ kg/m^3$ and its Young's modulus is $9.27 \times 10^{10} \ Pa$. What will be the fundamental frequency of the longitudinal vibrations in $kHz$?

DifficultJEE MAIN 2018

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Mention the audible frequency range for humans.

Medium

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For a particular sound wave propagating in air, a path difference between two points is $0.54 \, m$ which is equivalent to a phase difference of $(1.8 \pi)$. If the velocity of the sound wave in air is $330 \, m/s$, the frequency of this wave is: (in $Hz$.)

MediumMHT CET 2022

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$A$ firecracker exploding on the surface of a lake is heard as two sounds a time interval $t$ apart by a man on a boat close to the water surface. Sound travels with a speed $u$ in water and a speed $v$ in air. The distance from the exploding firecracker to the boat is

Similar Questions

The 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 are

$A$ sound wave of frequency $160 \,Hz$ has a velocity of $320 \,m/s$. When it travels through air, the particles having a phase difference of $90^{\circ}$ are separated by a distance of: (in $cm$)

$A$ granite rod of $60 \ cm$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^3 \ kg/m^3$ and its Young's modulus is $9.27 \times 10^{10} \ Pa$. What will be the fundamental frequency of the longitudinal vibrations in $kHz$?

Mention the audible frequency range for humans.

For a particular sound wave propagating in air, a path difference between two points is $0.54 \, m$ which is equivalent to a phase difference of $(1.8 \pi)$. If the velocity of the sound wave in air is $330 \, m/s$, the frequency of this wave is: (in $Hz$.)

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