Physics 198
Homework 14
Due October 20
1. How does the jnd for pitch generally compare to the critical bandwidth?
Solution:
Critical bandwidth is roughly equal to 30 difference jnd’s at the same frequency.
2. How does the pitch of a 200Hz tone depend on sound level?
Solution:
Early work by Stevens indicated shifts in pitch as large as two semitones as the sound level of
pure tones increased from 40 to 90dB. Tones of low frequency were found to fall in pitch with
increasing intensity; tones of high frequency rise in pitch with increasing intensity; tones of
middle frequency show little change.
From Figure 7.3, we see that 200Hz frequency falls about 30 cents with increasing intensity from
40 to 90dB.
3. What pitch will generally be heard when tones of 800, 1000, and 1200 Hz are sounded
together?
Solution: The pitch of 200Hz will generally be heard. This is virtual fundamental.
4. Discuss the advantages and disadvantages to performing musician of possessing absolute
pitch.
Solution:
The absolute pitch is the term that refers to the ability to recognize and define the pitch of a tone
without the use of a reference tone.
The advantages of absolute pitch are fairly clear. The musician could simply start singing on
pitch, tune his/her instrument without a tuning device, etc.
The disadvantage is that it is painful for such a person to sing or play along with other people
for a pitch standard that is off a little, for instance, in group of people that just start singing.
5. Compare the tension in a violin string tuned to a standard A (440 Hz) with the tension in the
same string tuned to match Handel’s tuning fork (422 Hz).
Solution:
T
The frequency dependence on tension is given by equation: f 
2
f
T
T f 
For the same string: 1  1  1   2  .
f2
T2
T2  f1 

2
.
T1  440 

  1.087
T2  422 
Physics 198
Homework 14
Due October 20
6. What are frequencies of the first four harmonics in a 300 Hz square wave?
Solution:
From Figure 7.11, we can find that square wave had the frequency f, 3f, 5f, 7f, etc. So the first
four harmonics are 300Hz, 900Hz, 1500Hz, and 2100Hz.