EQUATIONS

THE THRESHOLD OF HEARING CHART (IN DECIBELS).

TABLE OF EQUATIONS FOR OPEN/CLOSED ENDED WAVES!

OTHER IMPORTANT EQUATIONS YOU WILL NEED

Examples:

1.  The first formula... there is a good and a bad part....the bad part you will use it a lot. The good part is that the formula is very easy...

Let's say the velocity is 50m/s. Now, let's say the frequency is 10 Hz.  (Never forget the units!!)

Now, all you do is divide.

(50m/s) / 10Hz= 5nm The wavelength is 5nm!!!

2.  The second formula is pretty simple as well.

Let's say the sound in air is 500m/s. Just by knowing that you can solve the equation.

500m/s-331m/s=(169m/s)/.6=281.7C

3.  The last formula is the most difficult one of all....but not that hard, right?  The hard part is understanding what goes where...and we will help you with that.

The doppler effect is actually a very simple equation to use, in terms of filling in the values.  The hard part lies in deciding whether to make the value positive or negative.

When the source is moving toward the observer, the negative sign is used.  When the source is moving away from the observer, the positive sign is used.

Sample

A 300-Hz sound wave is coming toward you with a speed of 340 m/s.  If you were moving towards the source at 30 m/s, what frequency do you hear?  (Hint:  Consider the change in the period rather than in the frequency.)

wavelength=v/f=(340 m/s)/(300 s)=1.13 m

The wavelength is the distance between crests, and the distance is approaching you with a relative speed of 370 m/s.  The time between crests, at your ear, is, from the equation v=d/t.

T_o=wavelength/v_o=(1.13 m)/(370 m/s)=3.05 x 10^-3 s

This is the period of the wave as you hear it.  Its frequency is the reciprocal of the period, 327 Hz.

Putting this problem in algebraic form creates a formula for the Doppler effect.  Remember, velocity times the period gives the wavelength.

Sample 2

frequency_emitted=200 Hz
velocity_source=10 m/s
velocity_wave=350 m/s
velocity_observer=0 m/s

f=(200 Hz)[(350 m/s + 0 m/s)/(350 m/s - 10 m/s)]
f=206 Hz (coming)

f=(200 Hz)[(350 m/s - 0 m/s)/(350 m/s + 10 m/s)]
f=194 Hz (going away)