Beats — Prelims Questions

Two tuning forks A and B produce 5 beats per second when sounded together. Tuning fork A is in unison with a 0.5 m long string fixed at both ends, vibrating in its fundamental mode. The tension in the string is $100,\text{N}$ and its linear mass density is $0.01,\text{kg/m}$. When tuning fork B is loaded with wax, the beat frequency decreases to 2 beats per second. What is the original frequency of tuning fork B?

Two sound waves are represented by $y_1 = 3 sin(500pi t)$ and $y_2 = 3 sin(506pi t)$. What is the beat frequency produced by their superposition?

Which of the following conditions is NOT essential for the clear observation of beats?

A tuning fork of unknown frequency produces 6 beats per second with a standard fork of 300 Hz. When the unknown fork is filed, it produces 4 beats per second with the same standard fork. What is the original frequency of the unknown tuning fork?

Two organ pipes, open at both ends, have lengths $L_1 = 1.0,\text{m}$ and $L_2 = 1.01,\text{m}$. If the speed of sound in air is $330,\text{m/s}$, what is the beat frequency produced when they are sounded in their fundamental modes?

Two sound waves of frequencies 320 Hz and 324 Hz are superimposed. What is the frequency of the resultant wave that determines its perceived pitch, and what is the beat frequency?