Peoples Physics Book Version-2

http://www.ck12.org Chapter 12. Wave Motion and Sound Version 2

12.5 Examples

Wavelength, Frequency, and Velocity

Question: A 120cm long string vibrates as a standing wave with four antinodes. The wave speed on the string is
48m/s. Find the wavelength and frequency of the standing wave.

Answer: We will solve for the wavelength first. The wavelength will then allow us to solve for the frequency.

Since there are 4 antinodes, there are two complete waves (see diagram above). Therefore, one complete wavelength
must equal to half the length of the string

λ=

120cm

2

=60cm

Now that we have both the velocity and the wavelength of the wave we can solve for the frequency using the equation

v=fλ

Now we simply solve for the frequency and then plug in the known values.

v=fλ=

v

λ

Before we plug in the known values, we need to convert the wavelength from centimeters to meters. This will allow
us to cancel the units.

λ=60cm×

1m

100cm

=.6m

Now we can solve for the frequency.

f=

v

λ

=

48m/s

.6m

=80Hz

The Doppler Effect

Question: How fast would a student playing an A note (440Hz) have to move towards you in order for you to hear
a G note (784Hz)?

Answer: We will use the Doppler shift equation for when the objects are getting closer together and solve for the
speed of the student (the source).

fo=f(

v+vo

v−vs

)⇒fo×(v−vs) =f×(v+vo)⇒v fo−vsfo=f×(v+vo)⇒vs=−(

f×(v+vo)−v fo

fo

)

Now we plug in the known values to solve for the velocity of the student.

vs=−(

f×(v+vo)−v fo

fo

) =−(

440Hz×(343m/s+0m/s)−343m/s×784Hz

784Hz

) =151m/s