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Chapter 16: Q80P (page 477)

When played in a certain manner, the lowest resonant frequency of a certain violin string is concert A (440 Hz). What is the frequency of the (a) second and (b) third harmonic of the string?

Short Answer

Expert verified
  1. Frequency of second harmonic is 880 Hz
  2. Frequency of third harmonic is 1320 Hz

Step by step solution

01

Given data 

Lowest frequency isf1=440Hz

02

Understanding the concept of fundamental frequency

We have to usetheformula for nth harmonic frequency which is n timesthefundamental frequency.

Formula:

The frequency of oscillation of n-loops, fn=n脳v2L........1

03

Step 3(a): Calculation for second harmonic frequency

The lowest frequency is given. It means that the first harmonic frequency is 440 Hz , and using equation (1) and the frequency, it is given as:

440=v2L......2

Now the second harmonic frequency using equations (1) and (2) is given as follows:

role="math" localid="1660993667219" f2=2脳v2L=2脳440=880Hz

Hence, the value of second-harmonic frequency is 880 Hz

04

Step 4(b): Calculation of third harmonic frequency

Third harmonic using equations (1) and (2) is given as follows:

f3=3脳v2L=3脳440=1320Hz

Hence, the value of third-harmonic frequency is 1320 Hz

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