Question bank: Waves: Beats

In the music industry, the precise tuning of instruments is a crucial factor for the quality of performances. During a recording session, a sound technician notices that a cello and a piano, both properly tuned to 440 Hz, produce a combined sound that exhibits periodic variations in sound intensity. By analyzing the phenomenon, the technician identifies that the resulting sound is a beat, which occurs due to the slight difference in frequencies between the sound waves emitted by each instrument. The intensity of the combined sound varies between the minimum and maximum 4 times per second. Considering this situation and knowing that the frequencies of the cello and the piano are respectively fV and fP, we want to determine the beat frequency (fb) that these instruments are producing. What is the beat frequency between the sound waves emitted by the cello and the piano, assuming that the difference between their frequencies is 3 Hz?

During an interdisciplinary study on acoustics and musical perception, a group of 3rd-year high school students encounters the following situation: a keyboardist is tuning his instrument for a performance with a group of classical musicians. When playing a fixed reference note, the keyboardist perceives a beating with a note emitted by a tuning fork, which oscillates 2.5 times per second. Considering that the keyboardist adjusts his instrument to minimize the number of perceived beats and knowing that the fundamental frequency of the tuning fork is 440 Hz (standard tuning of the reference tuning fork), what should be the frequency of the keyboard to achieve the desired tuning, and how many beats will the keyboardist hear per second if the frequency difference between the notes causing the beating is strictly related to the perceived beating frequency?

João and Maria are in an experimental physics laboratory studying the phenomenon of sound beats. They use two tuning forks with close frequencies, the first tuning fork producing a frequency of 340 Hz and the second one producing a frequency of 346 Hz. (a) Determine the beat frequency between them. (b) Explain what happens to the amplitude of the resulting sound waves during a complete beat cycle. (c) Calculate the time required for a complete beat cycle to occur.

Two tuning forks, A and B, emit sound waves with frequencies of 300 Hz and 306 Hz, respectively. They are brought close to each other so that their waves add up. Determine the frequency of the resulting beat from the interference between the waves emitted by A and B.

Two musical instruments emit sound waves of frequencies f1 = 440 Hz and f2 = 442 Hz, respectively. The waves propagate through the air and reach a point P. Determine the frequency of the beats perceived at P, considering the speed of sound in the air as 340 m/s. Additionally, explain the phenomenon of beats and how it is related to the difference in frequency between the sound waves emitted by the instruments.