Question

I am stuck with both of these questions. Thanks in advanced!

1. If one tone has a frequency of 110 Hz and another tone is played near it with a tone of 113 Hz, the beat frequency is ___ Hz

2. A standing wave has 3 nodes in a string 20 m long. The wavelength of this wave is __ m rounded to the first decimal place

Answer 1

1) 3 Hz,
the difference frequency
sin a + sin b = 2 sin .5(a+b) cos.5 (a-b)
or
twice the average frequency times half the difference frequency
YOU HEAR TWO maxima per cycle (he square of the amplitude so you hear F1-F2 nor (1/2) (F1-F2)

Answer 2

2 I have no idea if the nodes at the end count as two of the three
I will assume yes so we have one node in the middle, the second harmonic

Adjacent nodes are (1/2) lambda apart
so the length of the string is a wavelength