A tuning fork of frequency n produces x beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

Step-by-step solution

Let the frequency of the tuning fork be n and the frequency of the sonometer string be f . The number of beats per second is given by x = |f - n| . This implies f = n + x or f = n - x . The frequency of a sonometer string is directly proportional to the square root of its tension ( f T ). When the tension in the string is slightly increased, its frequency f increases. If f = n + x , an increase in f will increase the difference |f - n| , resulting in more beats per second. If f = n - x , a slight increase in f will