A sonar pulse has a wavelength of 3.0 cm. If the pulse has speed in water of 1,500 m/s, what is its frequency?
1 Answer
Explanation:
The universal wave equation states that the velocity of a wave is the product of its wavelength and its frequency.
Mathematically speaking,
#color(blue)(|bar(ul(color(white)(a/a)v=lambdafcolor(white)(a/a)|)))#
#ul("where")# :
#v=# velocity of wave (metres per second)
#lambda=# wavelength (metres)
#f=# frequency (hertz or reciprocal seconds)
Step 1
Convert the given wavelength from centimetres into metres.
#3.0color(white)(i)cmxxm/(100color(white)(i)cm)#
#=3.0color(red)cancelcolor(black)(cm)xxm/(100color(red)cancelcolor(black)(cm))#
#=0.030color(white)(i)m#
Step 2
Rearrange for frequency,
#v=lambdaf#
Becomes,
#f=v/lambda#
Step 3
Substitute your known values to solve for the frequency of the pulse.
#f=(1500color(white)(i)m/s)/(0.030color(white)(i)m)#
#f=50000color(white)(i)Hz#
Rounding off the value to two significant figures,
#f=color(green)(|bar(ul(color(white)(a/a)color(black)(5.0xx10^4color(white)(i)Hz)color(white)(a/a)|)))#