An 80-cm -long steel string with a linear density of 1.0 g / m is under 200 N tension. It is plu

step 1 Hi everyone, this is the problem based or static base reduced in a stressed string. Here it is g

An 80-cm -long steel string with a linear density of 1.0 g /...

An $80-\mathrm{cm}$ -long steel string with a linear density of $1.0 \mathrm{g} / \mathrm{m}$ is under $200 \mathrm{N}$ tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a $20^{\circ} \mathrm{C}$ room?

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Key Concepts

Relationship between Frequency, Wavelength, and Wave Speed in a Medium

This principle connects the properties of a propagating wave through a medium, described by the formula v = f?, where v is the wave speed, f is the frequency, and ? is the wavelength. When transitioning from the vibration on the string to the sound wave in air, the frequency remains constant, and the wavelength of the sound is found by dividing the speed of sound in air by that frequency.

Fundamental Frequency of a Vibrating String

The fundamental frequency is the lowest natural frequency at which a string vibrates when fixed at both ends. In this mode, the wavelength of the vibration is twice the length of the string (? = 2L), and the frequency is determined by the wave speed on the string and its length using the relation f = v/(2L). This is a key idea in the study of standing waves and musical acoustics.

Wave Speed on a Stretched String

This concept refers to the speed at which transverse waves travel along a string under tension. It is determined by the tension in the string and its linear mass density according to the formula v = ?(T/?). This relationship is central to understanding how changes in tension or mass per unit length affect wave propagation in a medium like a string.

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