A sonar pulse has a wavelength of 3.2 cm and a speed of 1,500 m/s in water. What is the frequency of the pulse? (

Explanation:

The universal wave equation states that the velocity of a wave is the product of its wavelength and its frequency.

Mathematically speaking,

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

a

v

=

λ

f

a

a

∣

∣

−−−−−−−−−−−

where

−−−−−

:

v

=

velocity of wave (metres per second)

λ

=

wavelength (metres)

f

=

frequency (hertz or reciprocal seconds)

Step 1

Convert the given wavelength from centimetres into metres.

3.0

i

c

m

×

m

100

i

c

m

=

3.0

c

m

×

m

100

c

m

=

0.030

i

m

Step 2

Rearrange for frequency,

f

, in the universal wave equation.

v

=

λ

f

Becomes,

f

=

v

λ

Step 3

Substitute your known values to solve for the frequency of the pulse.

f

=

1500

i

m

s

0.030

i

m

f

=

50000

i

H

z

Rounding off the value to two significant figures,

f

=

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

a

5.0

×

10

4

i

H

z

a

a

∣

∣

−−−−−−−−−−−−−−−−