The speed [tex]v[/tex] of a wave (the sound in this case) is given by the following formula:
[tex]v=f.\lambda[/tex] (1)
Where:
[tex]f=100kHz=100(10)^{3}Hz[/tex] is the frequency
[tex]\lambda[/tex] the wavelength
It is known that the speed of sound in water at [tex]20\ºC[/tex] is:
[tex]v=1482\frac{m}{s}[/tex]
So, we only have to find [tex]\lambda[/tex] from (1):
[tex]\lambda=\frac{v}{f}[/tex] (2)
[tex]\lambda=\frac{1482\frac{m}{s}}{100(10)^{3}Hz}[/tex]
Knowing [tex]1Hz=\frac{1}{s}[/tex]:
[tex]\lambda=0.01482m[/tex]
But we were asked to find the wavelength in cm and we have to make the conversion:
[tex]\lambda=0.01482m.\frac{100cm}{1m}=14.82cm[/tex]
Hence:
[tex]\lambda=14.82cm[/tex]
