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4. A tuning fork is held over a resonance tube, and resonance occurs when the surface of the water is 12 cm below the top of the tube. Resonance occurs again when the water is 34 cm below the top of the tube. If the air temperature is 23 ˚C, find the frequency of the tuning fork.

Respuesta :

As we know that speed of sounds is given as

[tex]v = 332 + 0.6t[/tex]

here we know that

t = 23 degree C

now from above equation we will have

[tex]v = 332 + (0.6)(23)[/tex]

[tex]v = 345.8 m/s[/tex]

now we also know that distance between two consecutive resonance length is half of the wavelength

[tex]L_2 - L_1 = \frac{\lambda}{2}[/tex]

[tex]34 - 12 = \frac{\lambda}{2}[/tex]

[tex]\lambda = 44 cm[/tex]

now we know that

[tex]frequency = \frac{speed}{wavelength}[/tex]

[tex]f = \frac{345.8}{0.44} = 786 Hz[/tex]

so frequency will be 786 Hz

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