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ICSE Class 10 Answered

What adjustments would you make for tuninga stringed instrument for it to emit a note of desired frequency?

Asked by kumersingh1965 | 05 Aug, 2022, 06:56: PM
Expert Answer
In string instruments, tuning of frequency is done by adjusting the tension T in the string and length begin mathsize 16px style l end style of the vibrating part of the string.
In string instruments , wavelength λ of the sound wave produced by string is given as
 
λ = ( 2 begin mathsize 16px style l end style / n ) ............................ (1)
where n is number of harmonics
 
frequency f of sound wave ,  f = v / λ .............................. (2)
 
where v is velocity of transverse wave in string .Velocity v of transverse wave in string is given as
 
begin mathsize 14px style v space equals space square root of T over mu end root end style  ................................... (3)
where T is tension in the string and μ is linear mass density ( mass per unit length )

 
From eqn.(1) and (2) , we get
 
f = n × ( v / 2begin mathsize 16px style l end style
 
From above expression , we know that frequency depends on velocity v of transverse wave in the string and lenegth begin mathsize 16px style l end style .
velocity of transverse wave in the string is proportional to square root of tension T in the string.
 
Hence tuning of instrument to get desired frequency is done by adjusting tension T and length begin mathsize 16px style l end style of vibrating part of string .

Answered by Thiyagarajan K | 06 Aug, 2022, 08:12: AM
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