Question

5. [5pt] A xylophone (or glockenspiel) is a percussion instru- ment with keys made from metal plates of different lengths. When a key is hit with a mallet, it vibrates with its funda- mental standing wave mode, which determines the frequency of sound produced. Think of the keys as "strings with free ends", because the ends of the metal plates are free to oscillate. Assume that the E-key (1318.5 Hz) is 10.00 cm long and vi- brates at its fundamental frequency. a) How long is the G-key (1568.0Hz)? [ans. 8.41 cm b) What is the phase speed of waves in the keys? (ans. 264 m/s

Answer 1

a)

v = phase speed of waves = ?

For the E-key :

f_e = fundamental frequency in E-key = 1318.5 Hz

L = length of the key = 10 cm = 0.10 m

fundamental frequency is given as

f_e = v/(2L)

inserting the values

1318.5 = v/(2 x 0.1)

v = 264 m/s

For the G-key :

f_g = fundamental frequency in G-key = 1568 Hz

L' = length of the key = ?

fundamental frequency is given as

f_g = v/(2L')

inserting the values

1568 = 264/(2 L')

L' = 0.0841 m

L' = 8.41 m

b)

v = 264 m/s