Question

The longest bar on the xylophone is 18.30 cm. How long should the bar a Perfect Fifth higher be?

	A.	25.88 cm
	B.	12.20 cm
	C.	22.41 cm
	D.	14.94 cm

I have a metal bar that is 17.3 cm long. The fundamental frequency is 235 Hz. Which of the following frequencies does NOT correspond to a higher mode of vibration of the bar?

	A.	940.0
	B.	648.6
	C.	2098.6
	D.	1269.0

A vibrating bar has a fundamental frequency of 440 Hz. Find the frequency of the 3rd overtone and bring it down by octaves until you are in the octave starting with the fundamental. Note, 2.76f is the first overtone.

What interval does the new note make with the fundamental?

	A.	Whole step
	B.	Half step
	C.	Major third
	D.	Perfect fourth

Answer 1

(a) Given that, longest bar in the xylophone = 18.30 cm=

say length of the bar giving perfect fifth frequency =

we know that, perfect fifth frequency correspond to frequency ratio of 3:2 ie

in Case of xylophone the relation between frequency and length of the bar is given as

so here

(b) length of the metal bar = 17.3 cm

fundamental frequency (f) = 235 Hz

for a free bar, the fundamental vibration frequency is given by

where L - length of the bar

Y - young's modulus

a - thickness of the bar

d - density of the bar

the overtunes are given by

thus, the frequencies are given by

So, 940 Hz does not correspond to any higher modes of vibration.

(c) fundamental frequency = 440 Hz = F₁

3rd over tune frequency =

no of octaves = = 3.16= no of intervals

This interval corresponds to major third.