Two tuning forks are generating sounds of wavelengths 34.4 cm and 33.94 cm. How many beats are produced each second by the two tuning forks? The speed of sound is 340 m/sec. A. 18
B. 22
C. 14
D. 27

When you mix two waves, there are two beats produced.  The frequencies of the beats are (the sum) and (the difference) of the frequencies of the two original waves.  So we have to find the frequencies of these two forks.

Frequency = (speed) / (wavelength)

Fork #1: Frequency = (344 m/s) / (0.337 m) =  1020.8 Hz

Fork #2: Frequency = (344 m/s) / (0.3127 m) = 1100.1 Hz

The two beat frequencies are  2120.9 Hz  and  79.3 Hz.

From the choices allowed, the one they want you to pick is  80 Hz .  

Explanation:

This credit goes all to AL2006

increase masses, decrease separation

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.