Physics 198
Homework 20
Due November 17
1. Why are the bass strings of a piano wrapped with wire?
Solution:
The bass strings of a piano are wrapped to increase the mass of the string kipping small radius
and big tension. Bigger mass leads to lower frequency, but bigger radius increase inharmonicity,
and will require bigger force for the same tension.
2. What is the function of a piano bridge?
Solution:
The main function of the piano bridge is to transfer the energy from strings to soundboard.
3. Suppose that all strings of a piano were of the same material and also had the same diameter
and tension. If the longest string (A0) were 2.00 m in length, how long would the highest Astring (A7) have to be? Is this practical?
Solution:
The ratio of frequencies A7 and A0 is
f  A7 
 2 7  128 .


f A0
L A7    A7  f  A0 
f  A0 


 L A7   L A0 
 200cm 128  1.56cm
L A0    A0  f  A7 
f  A7 
Of course this is not practical.
4. If a particular string on a harpsichord has one-third the diameter and one –tenth the tension of
the corresponding string on a piano, which string will be longer? What will the ratio of length
be? Assume that both strings are steel. (See Sections 3.2 and 4.4)
Solution:
For strings
v
1
F

v
,   m L  V L  r 2 , and f1 

2L 2L
fh  f p 
1
2 Lh
Piano string is longer.
Fh
1

2
2L p
rh
Fp
r
2
p

Lp
Lh
F


rh
rp

1
F
.
2 L r 2
Fp
Fh

1
10  1.054
3