question_answer

A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before                                                        [NCERT 1984]

A)            460 Hz                                     

B)            470 Hz

C)            480 Hz                                     

D)            490 Hz

Correct Answer: B

Solution :

                   If suppose nS = frequency of string \[=\frac{1}{2l}\sqrt{\frac{T}{m}}\] nf = Frequency of tuning fork = 480 Hz x = Beats heard per second = 10 as tension T increases, so nS increases (­) Also it is given that number of beats per sec decreases (i.e. x¯) Hence nS­ ? nf  = x¯        ... (i)                Wrong              nf  ? nS­ = x¯        ... (ii)              Correct Þ nS = nf ? x = 480 ? 10 = 470 Hz.