$(a)$ The sound of an explosion on the surface of a lake is heard by a boatman $100 \ m$ away and a diver $100 \ m$ below the point of explosion. Of the two persons mentioned (boatman or diver),who would hear the sound first and why?
$(b)$ Calculate the wavelength of a sound wave whose frequency is $220 \ Hz$ and speed is $440 \ m \ s^{-1}$ in a given medium.
$(b)$ Calculate the wavelength of a sound wave whose frequency is $220 \ Hz$ and speed is $440 \ m \ s^{-1}$ in a given medium.
(B) The diver will hear the sound first. This is because the speed of sound in water (a liquid medium) is significantly higher than the speed of sound in air (a gaseous medium). Since the distance is the same for both,the sound travels faster through the water to reach the diver.
$(b)$ Given:
Frequency $(v) = 220 \ Hz$
Speed $(V) = 440 \ m \ s^{-1}$
Formula: $V = v \times \lambda$
Therefore,wavelength $(\lambda) = V / v$
$\lambda = 440 / 220 = 2 \ m$
The wavelength of the sound wave is $2 \ m$.
$(b)$ Given:
Frequency $(v) = 220 \ Hz$
Speed $(V) = 440 \ m \ s^{-1}$
Formula: $V = v \times \lambda$
Therefore,wavelength $(\lambda) = V / v$
$\lambda = 440 / 220 = 2 \ m$
The wavelength of the sound wave is $2 \ m$.
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