Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously.
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Since f beat = f a – f b , the possible frequencies are 440.0 Hz ± 1.5 Hz = 438.5 Hz. or 441.5 Hz.
The tension is proportional to the square of the frequency. Therefore T ∝ f 2 and 
T ∝ 2f 
f. So 
= 
.
(i) 
= 
= 6.82 × 10 –3 .
(ii) 
= 
= – 6.82 × 10 –3 .
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