A 75.0-cm-long wire of mass 5.625 g is tied at both ends and adjusted to a tension of 35.0 N. When it is vibrating in its second overtone, find (a) the frequency and wavelength at which it is vibrating and (b) the frequency and wavelength of the sound waves it is producing.

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aristocles aristocles · Answer 1 · 2019-07-19T03:56:35+02:00

Answer:

Part a)

wavelength = 50 cm

frequency = 136.6 Hz

Part b)

wavelength = 2.48 m

frequency = 136.6 Hz

Explanation:

As we know that linear mass density of the wire is given as

[tex]\lambda = \frac{m}{L}[/tex]

[tex]\lambda = \frac{5.625 \times 10^{-3}}{0.75}[/tex]

[tex]\lambda = 7.5 \times 10^{-3} kg/m[/tex]

now we know that tension in wire is given by

T = 35 N

so the speed of wave in the string is given as

[tex]v^2 = \frac{T}{\lambda}[/tex]

[tex]v = 68.3 m/s[/tex]

Part a)

now wire is vibrating in second overtone

so here we have

[tex]\frac{3(wavelength)}{2} = 75 cm[/tex]

[tex]wavelength = 50 cm[/tex]

now frequency is given as

[tex]f = \frac{v}{wavelength}[/tex]

[tex]f = 136.6 Hz[/tex]

Part b)

Frequency will remain same as it depends on source only

so frequency of sound wave will be f = 136.6 Hz

also for wavelength we have

[tex]wavelength = \frac{v}{f}[/tex]

[tex]wavelength = \frac{340}{136.6}[/tex]

[tex]wavelength = 2.48 m[/tex]