# a) What are the three longest wavelengths for standing waves on a 210 cm long string that is...

## Question:

a) What are the three longest wavelengths for standing waves on a 210 cm long string that is fixed at both ends?

b) If the frequency of the second longest wavelength in part a) is 45.0 Hz , then what is the frequency of the third longest wavelength?

## Longest Wavelengths Formed on a Stretched String:

On a string stretched under some tension *T*, a number of frequencies like first, second, third, etc harmonics are possible when excited with suitable frequencies that match with the frequency of oscillation of the respective harmonics. First harmonic is the first possible frequency of oscillation and the higher harmonics are integer multiples of it. The fundamental frequency of a wave on a string of length *L* is {eq}\displaystyle F_1 = \dfrac { v } { 2 L }
{/eq}. Here *v* is the speed of the wave on the string.

## Answer and Explanation: 1

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**Given points**

- Length of the string {eq}L= 2.10 m {/eq}

- Frequency of the second longest wavelength or second harmonics {eq}F_2 = 45.0 \ \ ...

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Chapter 5 / Lesson 19Standing waves are a result of wave interference. Explore the lesson to learn about the properties of standing waves, find their formulas, and see some examples.

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