Question

A tuning fork of a frequency 480Hz produces 10 beats per second when sounded with a vibrating

(a) 460Hz
(b) 480Hz
(c) 490Hz
(d) 470Hz

Answer 1

If the length of the string is L, the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic. Also beats are defined as the difference between the frequencies.

Complete step by step answer: Given that,

Frequency n = 480 Hz

Number of beat b= 10 b/s

WKT The frequency is directly proportional to the square root of tension.
If a slight increase in tension produces beats per second than before

The frequency of the vibrating string is
$$$$${n_2} = {n_1} + b$…… (1)${n_2} = 480 + 10$
=490Hz

Similarly,
${n_2} = {n_1} - b$……. (II)

   ${n_2} = 480 - 10$  
         =470Hz  

Hence, the frequency of the vibrating string will be 490 Hz.

Concluded correct option is C

Note: The beat frequency is when two sound waves with different frequencies come across each other, then their amplitude gets added and subtracted alternatively for a given time period. This leads to the growth of the sound to louder and softer.