You have a string with a mass of 0.0127 kg. You stretch the string with a force of 9.33 N, giving it a length of 1.93 m. Then, you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. What is the wavelength of the standing wave you create in the string? What is the frequency?

a. Wavelength = m
b. Frequency = Hz

Question

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-12-15T06:07:09+01:00

Answer:

wavelength = 0.968 m

frequency = 39.02 Hz

Explanation:

given data

mass = 0.0127 kg

force = 9.33 N

length = 1.93 m

to find out

wavelength and Frequency

solution

we know here linear density that is

linear density = [tex]\frac{mass}{length}[/tex] .........1

linear density = [tex]\frac{0.0127}{1.93}[/tex]

linear density = 6.5803 × [tex]10^{-3}[/tex] kg/m

so

wavelength will be here

wavelength = [tex]\frac{2L}{n}[/tex] ..............2

here n = 4 for forth harmonic

wavelength = [tex]\frac{2*1.93}{4}[/tex]

wavelength = 0.968 m

and

frequency will be for 4th normal mode of vibration is

frequency = [tex]\frac{4}{2L} \sqrt{\frac{tension}{linear\ density} }[/tex] ..........3

frequency = [tex]\frac{4}{2*1.93} \sqrt{\frac{9.33}{6.5803*10^{-3}} }[/tex]

frequency = 1.036269 × 37.654594

frequency = 39.02 Hz