124 NOTES, PROBLEMS AND EXERCISES

Musical Scales

226. The lowest tone of the human voice is about E-i; and the
highest about C3. Assuming the frequency of ili as 435 vibrations
per second, calculate the frequencies of these two notes on the equally
tempered scale.
^^bration of Bodies

227. A tuning-fork vibrating faster than a standard tuning-fork
of frequency 256 gives 2 beats per second when sounded with the
standard. A closed pipe of variable length resonates to this fork
when adjusted to a length of 33 cm. Calculate the velocity of sound.
228. The second overtone of an open organ pipe is of the same
pitch as the first overtone of a closed pipe. If the open pipe is 100
cm. long, what is the length of the closed pipe?

229. Find the wave length of the fundamental and the first over-
tone of a pipe 1 m. long closed at one end. Calculate the pitch of
each note at 16° C.
230. The dust piles in a Kundt's tube were 15 cm. apart in dry air
at 18° C. and 12.5 cm. in CO2 gas. What is the velocity of soimd in
the latter?

231. An alimiinum wire of 1 m. length and 1 nmi. diameter is
stretched by 2 kg. How large a weight must be used to stretch a
similar wire in order to produce 2 beats per second when the two
wires are soimded together?

LIGHT

Reflection

232. Find position, nature, and size of the image of an object of
2 cm. length placed (a) 60 cm., (6) 40 cm. from a concave mirror of
100-cm. radius.
233. Find the position, nature, and size of the image when an
object 3 cm. long is placed 20 cm. from a convex mirror of 30-cm.
