In an experiment on standing waves, a string 90 cm long is attached to the prong of an electrica

step 1 So in this question, we have this string that is 90 centimeter and it is oscillating in four loo

In an experiment on standing waves, a string 90 cm long is...

In an experiment on standing waves, a string 90 $\mathrm{cm}$ long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string at a frequency of 60 $\mathrm{Hz}$ . The mass of the string is 0.044 $\mathrm{kg} .$ What tension must the string be under (weights are attached to the other end) if it is to oscillate in four loops?

In an experiment on standing waves, a string 90 $\mathrm{cm}$ long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string at a frequency of 60 $\mathrm{Hz}$ . The mass of the string is 0.044 $\mathrm{kg} .$ What tension must the
string be under (weights are attached to the other end) if it is to oscillate in four loops?

Key Concepts

Linear Mass Density

Linear mass density (?) is defined as the mass per unit length of the string. It is a crucial parameter in determining the wave speed on the string, since a heavier string (larger ?) will typically have a slower wave speed for the same tension, affecting the formation of standing waves and their corresponding frequencies.

Wave Speed on a String

The speed of a wave travelling on a string is given by the formula v = ?(T/?), where T is the tension in the string and ? is its linear mass density. This relationship implies that an increase in tension will lead to a higher wave speed, which influences the frequency and wavelength of the standing waves produced.

Standing Waves

Standing waves are the result of interference between two waves traveling in opposite directions, which produces a fixed pattern of nodes and antinodes on the medium. In a string fixed at both ends, only specific wavelengths (and thus frequencies) produce such patterns, corresponding to the harmonic modes of the string.

Harmonic Modes

Harmonic modes refer to the quantized vibration patterns of a string fixed at both ends. Each mode is characterized by a specific number of half-wavelengths fitting into the string's length. For example, if there are four loops (or antinodes), this mode corresponds to a situation where there are a number of half wavelengths that determine the effective wavelength in the standing wave pattern.

Transcript

Please give Ace some feedback