# The Wave Equation ```The Wave Equation


The speed ( v ) that a wave pulse travels at and the frequency of the continuous
wave ( f ) determine the wavelength (  ) of the wave
speed = distance/time
[distance = , time is the period = T]
v=/T
v = wave speed [ms-1];  = wave length [m]; T = period [s];
v=f
f = frequency [Hz]
Example 1. Red light of frequency 3.95x1014 Hz has a wavelength of 760 nm.
What is the speed of light?
[760 nm = 760x10-9 m]
v = f = 3.95x1014(760x10-9)  3.00x108 ms-1
Example 2. Sound waves travel at 334 ms-1 in air. What is the wavelength of a
sound produced by a 256 Hz tuning fork?
v = f …  = v/f = 334/256  1.30 m
Example 3. A ripple tank generator is set at 24 Hz. Measurement of the ripple
wave produced has the distance between wavefronts as 2.5 cm.
What is the speed of the water waves?
f = 24 Hz [same as source] and
 = 0.025 m [distance between successive crests]
v = f = 24(0.025) = 0.60 ms-1
Example 4. An AM radio-wave has a wavelength of 100 metres. Given that radiowaves travel at the speed of light [3.0x108 ms-1], what is the
frequency of this radio signal [in MHz]?
 = 100 m
v = 3.0x108 ms-1
v = f … f = v/ = 3.0x108/100 = 3.0x106 Hz
f = 3.0 MHz
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