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

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)

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

No problem! I can help you with both of these questions. Let's start with the first one.

1. To find the beat frequency, we need to subtract the frequencies of the two tones. In this case, we have one tone with a frequency of 110 Hz and another tone with a frequency of 113 Hz.

So, the beat frequency can be calculated by subtracting the second tone frequency from the first tone frequency: Beat frequency = 113 Hz - 110 Hz = 3 Hz.

Therefore, the beat frequency is 3 Hz.

Now, let's move on to the second question.

2. A standing wave on a string is characterized by nodes and antinodes. Nodes are points in the wave that do not experience any displacement, while antinodes are points of maximum displacement.

In this case, we are told that the standing wave has 3 nodes in a string that is 20 m long.

To find the wavelength of the wave, we can use the relationship between wavelength, speed, and frequency. The formula is: wavelength = speed / frequency.

However, we are not given the frequency in this question.

However, we can use the concept of harmonic series for standing waves. In this case, a string with 3 nodes has a fundamental frequency and two harmonic frequencies (overtones).

The fundamental frequency is the lowest possible frequency for a standing wave on a given string. It corresponds to the first harmonic. The second harmonic corresponds to double the frequency of the fundamental, and the third harmonic corresponds to triple the frequency of the fundamental.

Therefore, if we consider the third harmonic, which would have 3 nodes, we know that the frequency of the third harmonic is three times the fundamental frequency.

To find the fundamental frequency, we can use the formula: fundamental frequency = speed / wavelength.

Since the fundamental frequency corresponds to the first harmonic, we can set it as f and consider the third harmonic as 3f.

Now, the third harmonic frequency is three times the fundamental frequency, so we can write: 3f = 3 * fundamental frequency.

Since wavelength is inversely proportional to frequency, we can write: wavelength for third harmonic = speed / (3 * fundamental frequency).

Given that the length of the string is 20 m and we have 3 nodes, we can express the wavelength in terms of the string length: wavelength for third harmonic = (2 * string length) / 3.

Now, we divide this wavelength by 3 to get the wavelength for the fundamental frequency: wavelength for fundamental frequency = [(2 * string length) / 3] / 3.

Finally, we can substitute the given values and calculate the wavelength: wavelength = [(2 * 20 m) / 3] / 3 ≈ 4.44 m (rounded to the first decimal place).

Therefore, the wavelength of this wave is approximately 4.44 meters when rounded to the first decimal place.