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
Jun 17, 2016

#5.0xx10^4color(white)(i)Hz#

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, #f#, in the universal wave equation.

#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)|)))#