Standing waves question with harmonics?

In summary, a person hums into a well and finds standing waves at frequencies of 42, 70, and 98 Hz. The speed of sound is given as 343m/s and the task is to determine the depth of the well. The solution involves considering the harmonic ratios between frequencies and identifying 42 Hz as the third harmonic. However, since it is not necessarily the fundamental frequency, the first approach of using wavelength and halving it cannot be applied. Further analysis is needed to determine the depth.
  • #1
Kratos321
20
0

Homework Statement



A person hums into the top of a well and finds that standing waves are established at frequencies of 42, 70 and 98 Hz. The frequency of 42 Hz is not necessarily the fundamental frequency. The speed of sound is 343m/s. How deep is the well?

Homework Equations



just harmonic ratios.

The Attempt at a Solution



i've no clue pls help. since we can't assume that 42Hz is the fundamental.

my first approach was to use the fundamental frequency. find the wavelength and then half of that would be the depth but i don't know how to do it if we can't assume.
 
Last edited:
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  • #2
Hint: Consider the ratio of one frequency to another, for all pairs.
 
  • #3
is this system open closed?
 
  • #4
ok so i figured out that the 42Hz is the third harmonic. now what shall i do?
 
  • #5
How did you figure out it was the third harmonic?
 

Related to Standing waves question with harmonics?

1. What are standing waves?

Standing waves are a type of wave that occurs when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This results in a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).

2. What are harmonics in standing waves?

Harmonics in standing waves refer to the specific patterns or modes of vibration that occur at different frequencies. The fundamental frequency, or first harmonic, is the lowest frequency at which a standing wave can occur. Higher harmonics are integer multiples of the fundamental frequency.

3. How are standing waves and harmonics related?

Standing waves and harmonics are closely related because harmonics are the different modes or patterns of vibration that occur in a standing wave. Each harmonic has a specific wavelength and frequency that determines its position in the standing wave.

4. What factors affect the formation of standing waves and harmonics?

The formation of standing waves and harmonics is affected by several factors, including the properties of the medium through which the wave travels (such as density and tension), the frequency and amplitude of the wave, and the boundary conditions of the medium (such as fixed or free ends).

5. What are some real-world applications of standing waves and harmonics?

Standing waves and harmonics have many practical applications, including in musical instruments, where different harmonics create different notes; in telecommunications, where standing waves are used to transmit signals; and in engineering, where they can be used to detect flaws in structures through resonance testing.

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