Download fn = f0 * (a)n

Natural Sciences 1 (ERTH 1030)
Question Set 4
These homework questions will be the subject of recitation during the week of October
5th. For full credit, the completed assignment must be turned in by 5 p.m. on Friday,
October 13th. Please be sure your work is neat and that you show enough detail for the
grader to follow your reasoning.
1. A) In physical terms, describe the way a Heat Engine works. B) How is this
different from the way an internal combustion engine works?
2. If a wave has a frequency of 2000 Hz, what is its period?
3. One wave has a frequency of 5 X 10-3 and wavelength X. If another wave
traveled at the same velocity and had a wavelength three times wider, what
would its period be?
4. You are swimming in the ocean. Your buddy is about 200 meters away, also
swimming. You are carrying a water-proof radio, through which the coast guard
informs you that there are sharks closing in! You yell for your friend to leave the
water immediately. Would your friend hear you sooner if the air was at 20°C or
at 30°C? How much sooner?
5. Why does sound travel faster through water than through air?
6. You are the sonar radar operator of a submarine. You are enjoying some coffee
when you see the blip of a torpedo closing in! The first time you see the blip it
takes 1.5 seconds for the signal to bounce off the torpedo and return to you. At
the next pass (t = 5 seconds), the blip takes 1.2 seconds to bounce back. At
what speed is the torpedo traveling? How long do you have to execute an
evasive maneuver?
7. Explain what a “BEAT” is in terms of waves. Your answer should include a
diagram and the words “Constructive Interference” and “Destructive
Interference”.
8. If you have two tuning forks of the same thickness but different lengths, why does
the one with the longest prongs have a lower sound?
9. Give two examples each of the following: A) transverse wave B) longitudinal
wave.
10. In western music, the notes have pitch values on the chromatic scale with 12
intervals called half-steps between equal tempered pitches (otherwise known as
equivalent notes). Equal temper tuning scheme is used to tune a keyboard
instrument so that each note is correctly pitched. Equal temper uses the
following relationship:
fn = f0 * (a)n
where fn is the frequency of the note at n half-steps away from f0, f0 is the
reference frequency, a is equal to (2)1/12 (the twelfth root of two), and n is the
number of half-steps from the reference frequency. The pitch known as an A4 (A
above middle C on a piano) is typically taken as the reference at a frequency (f0)
of 440 Hz. Please calculate the frequencies for:
A#4, which is 1 half-step above A4
G#, which is 1 half-step below A4
C5, which 3 half-steps above A4
A5 which is 12 half-steps above A4
A3 which is 12 half-steps below A4
What is the similarity between the frequencies A3, A4, A5? Why do these pitches
sound similar?